Model independent analysis of B → (1430)μ+μ−decay
-
Upload
ishtiaq-ahmed -
Category
Documents
-
view
223 -
download
4
Transcript of Model independent analysis of B → (1430)μ+μ−decay
JHEP02(2012)045
Published for SISSA by Springer
Received October 16 2011
Revised December 21 2011
Accepted January 23 2012
Published February 15 2012
Model independent analysis of B rarr Klowast
2(1430)micro+microminus
decay
Ishtiaq Ahmedab M Jamil Aslamabc Muhammad Junaidab and Saba Shafaqb
aNational Centre for Physics Quaid-i-Azam University Campus
Islamabad 45320 PakistanbDepartment of Physics Quaid-i-Azam University
Islamabad 45320 PakistancPhysics Department University of Alberta
Edmonton T6G 2G7 Alberta Canada
E-mail ishtiaqncpedupk jamilncpedupk mjunaidncpedupk
sabaqauedupk
Abstract A detailed study of the impact of New Physics (NP) operators with differ-
ent Lorentz structures which are absent in the Standard Model Hamiltonian on the
B rarr Klowast2 (1430)micro
+microminus decay is performed In this context the various observables such
as branching ratio forward-backward asymmetry of leptons lepton polarization asymme-
tries and the helicity fractions of the final state Klowast2 (1430) meson have been studied We
have examined the effects of new vector-axial vector scalar-pseudoscalar and tensor type
interactions for this decay B rarr Klowast2 (1430)micro
+microminus by using the constraints on different NP
couplings which come from the Bs rarr micro+microminus B rarr Xsmicro+microminus and B rarr Klowastmicro+microminus decays It
is found that the effects of V A SP and T operators are significant on the zero position of
AFB(q2) as well as on its magnitude In addition to this these NP operators also give sig-
nificant effects on the differential decay rate lepton polarization asymmetries and helicities
fractions of final state Klowast2 (1430) meson
Keywords Rare Decays Beyond Standard Model B-Physics
ccopy SISSA 2012 doi101007JHEP02(2012)045
JHEP02(2012)045
Contents
1 Introduction 1
2 B rarr Klowast
2(1430)micro+microminus operators and matrix elements 3
21 Standard model 3
22 New physics operators 4
23 Parametrization of matrix elements and form factors 5
24 Numerical constraints on NP parameters 6
3 Decay rate forward-backward asymmetry and lepton polarization a-
symmetries for B rarr Klowast
2(1430)micro+microminus decay 8
31 Differential decay rate 9
32 Forward-backward asymmetry 10
33 Lepton polarization asymmetries 10
34 Helicity fractions 12
4 Numerical Analysis 13
41 V A new-physics operators 15
42 SP new-physics operators 20
43 T operators and interference of SP and T operators 22
44 All NP operators together 26
5 Conclusions 30
1 Introduction
The wealthy data taken from the Tevatron experiments on Bs and the other B-factories
have reached to the luminosity where billions of B mesons will be produced which will help
us to enter into the precision era of B physics The Standard Model (SM) is enormously
successful in explaining most of the data to date However some discrepancies in the
predication of the SM have been observed in B decays [1ndash4] The pertinent examples are
(i) in B rarr Kπ decays it is difficult to account for all the experimental measurements of
CP asymmetry in neutral and charged modes within the SM [7] (ii) the B0s minus B0
s mixing
phase by the CDF and DO collaboration deviates from the SM prediction [5 6] (iii) the
isospin asymmetry between neutral and the charged decay modes of the B rarr Klowastℓ+ℓminus
decay also deviate from the SM [8 9] The Large Hadron Collider (LHC) is already up
and running where CMS ATLAS and LHCb have already started taking data while the
Super-B factories are on their way Therefore it is an ideal time to test the predictions of
SM and try to identify the nature of physics that is beyond SM
ndash 1 ndash
JHEP02(2012)045
In SM the zero crossing of the AFB(q2) in B rarr Klowastl+lminus is at a well determined
position which is free from the hadronic certainties at the leading order (LO) in strong
coupling αs [11ndash13] Recently the LHCb has announced the results of AFB for the decay
B rarr Klowastmicro+microminus that are close to the SM predictions They have collected over 300 events
for this decay with signal to background ratio above 3 which is the largest sample of such
decays in the world and is even cleaner than the sample used by the B factories These
results of AFB(B rarr Klowastmicro+microminus) are close to the SM predictions with slight error bars thus
they have overwritten the earlier measurements by Belle with better statistics [15] The
collaboration plans to continue to study the channel B rarr Klowastmicro+microminus in finer detail with
measurements that include more angular variables and expected to achieve high sensitivity
to any small deviation from the SM [15]
In order to incorporate the experimental predictions of different physical observables
in B rarr Klowastmicro+microminus this decay has been studied in SM and in number of different NP scenar-
ios [10 12 16ndash36] where NP effects display themselves through modification in the Wilson
coefficients as well as through the new operators Beside these models the general analysis
of B rarr Klowastmicro+microminus decay has also been performed which allow us to include all possible
NP effects like vector-axial vector (V A) scalar-pseudoscalar (SP ) and tensor-axial tensor
(TE) [37] This study has shown that the interference of V A operators among themselves
and with the SM operators is the cause of the larger magnitude of AFB(q2) as well as the
shift in the zero position of the AFB(q2) In addition to this it is also pointed out that the
SP and T operators not only influence the AFB(q2) but also give viable effects in other
physical observables
In general there are two ways to search NP which are considered to resolve anomalies
in the experimental measurements One is the direct search which can be achieved by
increasing the energies of colliders and find the predicted new particles but these particles
are quite massive and therefore hard to produced The other one is indirect search which
is comparatively easier ie to see how much different observables are affected by these new
particles The indirect searches require precise measurement of the observables for the
channel under consideration as well as need rigorous complementary studies
It is therefore indispensable to study the impact of NP on the different observables for
the decay channels other than the B rarr Klowastmicro+microminus With this motivation the B rarr Klowast2ℓ
+ℓminus
channel where Klowast2 is the excited state of Klowast with parity 2+ provide the same testing
ground to study the effects of the NP as B rarr Klowastmicro+microminus decay The exclusive B rarrKlowast
2 (1430)ℓ+ℓminus decay has been studied in the SM and some approaches beyond SM [38ndash46]
For example in refs [38 39] the form factors for B rarr Klowast2ℓ
+ℓminus are calculated using pertur-
bative QCD and LCSR approaches The analysis of different physical observable for this
decay is studied in various beyond SM scenarios like SM4 non-universal Z prime model Uni-
versal Extra dimension model and a model with the flipped sign of Ceff7 has been performed
in [40ndash42 45] The analysis of lepton polarization asymmetries of B rarr Klowast2ℓ
+ℓminus in the pres-
ence of new right-handed currents is done in [43 44] The analysis of polarized decay width
and forward-backward asymmetry by considering beyond SM operator basis is given in [46]
These studies show that like B rarr Klowastℓ+ℓminus decay this channel is also quite promising in
finding NP and will provide us some independent tests of the physics of the SM and beyond
ndash 2 ndash
JHEP02(2012)045
In this paper we will perform the study of B rarr Klowast2 (1430)micro
+microminus on the lines of ref [37]
and study the NP effects without restricting ourselves to any specific model Contrary to
B rarr Klowastmicro+microminus the decay B rarr Klowast2 (1430)micro
+microminus is not yet experimentally observed We have
taken into account the constraints from the different B decay mode such as Bs rarr micro+microminus
B rarr Xsmicro+microminus and B rarr Klowastmicro+microminus on different NP operator couplings allowed by the
most general lorentz structure of transition matrix elements In this paper we will also
incorporate bounds on the input parameters coming from the recent AFB measurements
at LHCb experiment for the decay B rarr Klowast(892)micro+microminus [15] With these new bounds we
will obtain better understanding of how these new physics operators affect branching ratio
zero-position of forward-backward asymmetry different lepton polarization asymmetries
and the helicity fractions of final state meson
The effects of these new operators couplings (VASPT) are significant to the zero
position of AFB(q2) as well as on its magnitude In addition to AFB these NP operators
also give significant effects on decay rate lepton polarization asymmetries and longitudinal
and transverse helicities of final state Klowast2 (1430) meson We hope that in the coming years
the LHCb experiment will collect around 64k events in the full range of q2 for an integrated
luminosity of 2fbminus1 [37] This would allow us to observe the B rarr Klowast2 (1430)micro
+microminus in the
SM and would also permit many of the additional tests of NP
The paper is organized as follows in section 2 the necessary hadronic inputs namely
basic Hamiltonian and form factors and constraints on the NP parameters are collected
Section 3 contains the analytic formulas for differential decay rates forward backward
asymmetry different polarizations (longitudinal normal and transverse) and the helicity
fractions of the final state Klowast2 (1430) meson Section 4 deals with the numerical analysis
and then conclusions are summarized in section 5
2 B rarr Klowast
2(1430)micro+microminus operators and matrix elements
21 Standard model
The semileptonic decay mode B rarr Klowast2 (1430)l
+lminus where l = micro for our case is governed
by the quark level transitions b rarr sl+lminus In SM the effective Hamiltonian corresponding
to this transition is given by
HSMeff = minus4GFradic
2V lowasttbVts
10sum
i=1
Ci(micro)Oi(micro) (21)
where Oi(micro)(i = 1 10) are four quark operators and Ci(micro) are the corresponding Wilson
coefficients Out of these 10 operators the O7 O9 and O10 are the relevant for B rarrKlowast
2 (1430)l+lminus decay and these can be written as
O7 =e
16π2[sσmicroν (msPL +mbPR) b]F
microν
O9 =e
16π2[sγmicroPLb]
(
lγmicrol)
O10 =e
16π2[sγmicroPLb]
(
lγmicroγ5l)
(22)
with PLR = (1plusmn γ5) 2
ndash 3 ndash
JHEP02(2012)045
In term of these operators the effective Hamiltonian for B rarr Klowast2 (1430)l
+lminus takes the
form
HSMeff = minusGFαradic
2πVtbV
lowastts
CSM9 (sγmicroPLb)(lγ
microl) + CSM10 (sγmicroPLb)(lγ
microγ5l)
minus2mbCSM7 (siσmicroν
qν
q2PRb)(lγ
microl)
(23)
where q2 is square of the sum of the momentum of final state leptons At the scale micro =
48GeV the SM Wilson coefficients takes the following values which are calculated at next-
to-next-to-leading order
Ceff7 = minus034 Ceff
9 = 4211 + Y (q2) C10 = minus4103 (24)
where Ceff7 = C7 minus C33minus 4C49minus 20C53minus 80C69 The function Y (q2) is given by
Y (z q2) = h(z q2)(3C1(micro) + C2(micro) + 3C3(micro) + C4(micro) + 3C5(micro) + C6(micro))
minus1
2h(1 sprime)(4C3(micro) + 4C4(micro) + 3C5(micro) + C6(micro))
minus1
2h(0 q2)(C3(micro) + 3C4(micro)) +
2
9(3C3(micro) + C4(micro) + 3C5(micro) + C6(micro)) (25)
with
h(z q2) = minus8
9lnz +
8
27+
4
9xminus 2
9(2 + x)|1minus x|12
ln∣
∣
∣
radic1minusx+1radic1minusxminus1
∣
∣
∣minus iπ for x equiv 4z2q2 lt 1
2 arctan 1radicxminus1
for x equiv 4z2q2 gt 1
h(0 q2) =8
27minus 8
9lnmb
microminus 4
9lnq2 +
4
9iπ (26)
and z = mcmb
22 New physics operators
The NP effects in semileptonic B meson decays can be established in two ways in one case
we can change the Wilson Coefficients but leave the operator basis same as that of the SM
and in other case we can add new operators too Here we do not restrict ourself to any
model and discuss all possible operators that corresponds to B rarr Klowast2 (1430)l
+lminus decays
In this scenario the total effective Hamiltonian for brarr sl+lminus can be written as
Heff = HSMeff +HV A
eff +HSPeff +HT
eff (27)
where HSMeff is given in eq (23) while [37]
HV Aeff =minus 4GFradic
2
α
4πV lowasttsVtb RV (sγmicroPLb) microγmicromicro+RA (sγmicroPLb) microγmicroγ5micro
+RprimeV (sγmicroPRb) microγmicromicro+Rprime
A (sγmicroPRb) microγmicroγ5micro
(28)
HSPeff =minus 4GFradic
2
α
4πV lowasttsVtb RS (sPRb) micromicro+RP (sPRb) microγ5micro
+RprimeS (sPLb) micromicro+Rprime
P (sPLb) microγ5micro
(29)
HTeff =minus 4GFradic
2
α
4πV lowasttsVtb
CT (sσmicroνb) microσmicroνmicro+ iCTE (sσmicroνb) microσαβmicroǫmicroναβ
(210)
ndash 4 ndash
JHEP02(2012)045
Here RV RA RV RprimeA RS RP R
primeS R
primeP CT and CTE are the NP effective couplings The
constraints on the numerical values of these NP coupling from different B meson decays
will be given later in this section
23 Parametrization of matrix elements and form factors
The exclusive B rarr Klowast2 (1430)l
+lminus decay involves the hadronic matrix elements of quark
operators which can be parameterized in terms of form factors These form factors are
written as
lang
Klowast2 (k ǫ) |sγmicrob|B(p)
rang
= minus 2V (q2)
mB +mKlowast
2
ǫmicroνρσεlowastναp
α
mBpρkσ (211)
lang
Klowast2 (k ǫ)
∣
∣sγmicroγ5b∣
∣B(p)rang
=2imKlowast
2A0(q
2)
q2εlowastναp
α
mBqνqmicro
+i(mB +mKlowast
2)A1(q
2)
mB
[
gmicroνεlowastναpα minus 1
q2εlowastναp
αqνqmicro]
minusiA2(q2)
εlowastναpαqν
mB(mB +mKlowast
2)
[
(pmicro + kmicro)minusm2
B minusm2Klowast
2
q2qmicro
]
(212)lang
Klowast2 (k ǫ) |sσmicroνqνb|B(p)
rang
= minus2iT1(q2)ǫmicroνρσ
εlowastναpα
mBpρkσ (213)
lang
Klowast2 (k ǫ)
∣
∣sσmicroνγ5qνb∣
∣B(p)rang
= T2(q2)[
(m2B minusm2
Klowast
2)gmicroνεlowastναp
α minus εlowastναpαqν(pmicro + kmicro)
] 1
mB
+T3(q2)εlowastναp
α
mBqν
[
qmicro minus q2
m2B minusm2
Klowast
2
(pmicro + kmicro)
]
(214)
lang
Klowast2 (k ǫ) |sb|B(p)
rang
=2V (q2)
(mB +mKlowast
2)(mb minusms)
ǫmicroνρσεlowastναp
α
mBpρkσ (215)
lang
Klowast2 (k ǫ)
∣
∣sγ5b∣
∣ B(p)rang
=2imKlowast
2A0(q
2)
q2εlowastναp
α
mB(mb +ms)qνqmicro (216)
lang
Klowast2 (k ǫ) |sσmicroνb|B(p)
rang
= minus2T1(q2)ǫmicroνρσ
εlowastναpα
mBpρkσ (217)
where p(k) is the momentum of the B(Klowast2 ) meson and εlowastνα is the polarization of the final
state Klowast2 (1430) meson In case of the tensor meson the polarization sum is given by [38]
Pmicroναβ =sum
εmicroν(p)εlowastαβ(p) =
1
2(θmicroαθνβ + θmicroβθνα)minus
1
3(θmicroνθαβ) (218)
with
θmicroν = minusgmicroν +kmicrokνm2
Klowast
2
(219)
Defining
εlowastν = εlowastναpαmB (220)
the resulting matrix elements for B rarr Klowast2 (1430) will look just like the B rarr V (eg Klowast
meson) transitions The form factors for B rarr Klowast2 (1430) transition are the non-perturbative
ndash 5 ndash
JHEP02(2012)045
F (q2) F (0) a b
V (q2) 016+002minus002 208 15
A0(q2) 025+004
minus004 157 01
A1(q2) 014+002
minus002 123 049
A2(q2) 005+002
minus002 132 149
T1(q2) 014+002
minus002 207 15
T2(q2) 014+002
minus002 122 034
T3(q2) 001+001
minus002 991 276
Table 1 B rarr Klowast
2 form factors in the light cone sum rules approach F (0) denotes the value
of form factors at q2 = 0 while a and b are the parameters in the parameterizations shown in
eq (221) [39]
quantities and are needed to be calculated using different approaches (both perturbative
and non-perturbative) like Lattice QCD QCD sum rules Light Cone sum rules etc Here
we will consider the form factors calculated in the LCSR approach [39] and their evolution
with q2 is given by
F (q2) =F (0)
1minus a(q2m2B) + b(q2m2
B)2
(221)
where the value of different parameters is given in table 1
The errors in the values of the form factors arise from number of input parameters
involved in their calculation in LCSR such as variations in the Boral parameters fluctuation
of threshold parameters errors in the b quark mass corrections from the decay constants
of involved mesons and from the Gengenbauer moments in the distribution amplitudes
It is worth mentioning here that it is possible to study this mode with the help of
QCD factorization which might discover additional sources of theoretical errors which are
overlooked in the simple form factor analysis As besides the factorizable contribution of
form factors which has been used here there are in principle non-factorizable contributions
to matrix elements as well [13] QCD factorization not only reduce the number of inde-
pendent parameters in heavy quark limit but also help us to compute the non-factorizable
corrections to B meson decays with the help of light-cone distribution amplitudes and
hard scattering kernel [53 54] The details of QCD factorization and its implications in
semileptonic and radiative B meson decays can be found in [13]
24 Numerical constraints on NP parameters
The constraints on NP parameters can be obtained from the branching ratios of B0s rarr
micro+microminus B0s rarr Xsmicro
+microminus and B0d rarr Kmicro+microminus [5 47ndash50] Due to the large hadronic uncertain-
ties the constraints obtained from the exclusive decay modes are somewhat weaker com-
pared to the inclusive ones The branching ratio of inclusive decay mode B rarr Xsmicro+microminus has
been measured by Babar [49] and Belle [50] and their measurements in low-q2 (1GeV2 le
ndash 6 ndash
JHEP02(2012)045
q2 le 6GeV2) and high-q2 (144GeV2 le q2 le 25GeV2) regions can be summarized as
B(B rarr Xsmicro+microminus)low q2 = (149plusmn 050+041
minus032)times 10minus6 (Belle)
(18plusmn 07plusmn 050)times 10minus6 (BaBar) (222)
(160plusmn 050)times 10minus6 (Average)
B(B rarr Xsmicro+microminus)high q2 = (042plusmn 012+007
minus007)times 10minus6 (Belle)
(050plusmn 025+007minus008)times 10minus6 (BaBar) (223)
(044plusmn 012)times 10minus6 (Average)
where q2 is the invariant mass squared of two muons and low-q2 region corresponds to
1GeV2 le q2 le 6GeV2 and high-q2 region corresponds to q2 ge 144GeV2
The constraints on the new V A couplings come mainly from B0d rarr Xsmicro
+microminus and B0d rarr
Kmicro+microminus [51] It has been shown in ref [51] that if RVA couplings are present only the
constraints on these couplings from above said decays came to be
10 le |RV + 36|2(47)2
+|RA minus 40|2
(48)2|RV + 28|2
(65)2+|RA minus 41|2
(66)2le 1 (224)
Similarly when we have only RprimeVA couplings the constraints on them from the same decay
will become [51]
22 le |RprimeV + 36|2 + |Rprime
A minus 40|2 le 566 |RprimeV |2 + |Rprime
A|2 le 17 (225)
These constraints are weekend when both RVA and RprimeVA couplings are present at the same
time In this case these new physics couplings are restricted to be
|RV + 28|2(65)2
+|RA minus 41|2
(66)2le 1 (226)
and
|RprimeV |2 + |Rprime
A|2 le 40 (227)
The limits on couplings corresponding to scalar-pseudoscalar (SP) operators comes
from the upper bound on B0s rarr micro+microminus which provides the limit
|RS minusRprimeS |2 + |RP minusRprime
P |2 le 044 (228)
This puts a sever constraint on the NP couplings if only RSP or RprimeSP are present However
under the condition where both types of operators are present RSP or RprimeSP these bounds
can be relaxed due to cancelation between the RSP and RprimeSP In this case B0
d rarr Xsmicro+microminus
and B0d rarr Kmicro+microminus can still bound these couplings and the stronger bound is obtained from
the measurement of later quantity which yields
|RS |2 + |RP |2 le 9 RS asymp RprimeS RS asymp Rprime
P (229)
Now the constraint on the NP tensor type couplings comes entirely from the inclusive
B0d rarr Xsmicro
+microminus decay In case when only tensor type operators are present the limits on
tensor type couplings are [51]
|CT |2 + |CTE |2 le 10 (230)
ndash 7 ndash
JHEP02(2012)045
In the present study we will examine B rarr Klowast2 (1430)micro
+microminus decays by using these NP
constraints
3 Decay rate forward-backward asymmetry and lepton polarization a-
symmetries for B rarr Klowast
2(1430)micro+microminus decay
In this section we are going to perform the calculations of some very interesting quantities
like the decay rate the forward-backward asymmetry the polarization asymmetries of
the final state lepton and the helicity fractions of the final state Klowast2 (1430) meson From
eq (27) it is straightforward to obtain the decay amplitude for B rarr Klowast2 (1430)micro
+microminus as
M(B rarr Klowast2 (1430)micro
+microminus) = minus GFα
2radic2π
VtbVlowastts
[
TmicroV lγmicrol + Tmicro
A lγmicroγ5l
+TS ll + TP lγ5l + Tmicroν
T lσmicroν l + iTmicroνE ǫmicroναβ lσαβl
]
(31)
with
TmicroV = minusF1ǫ
microναβεlowastνpKlowastαqβ + iF2εlowastmicro + iF3ε
lowast middot q(pB + pKlowast)micro + iF4εlowast middot qqmicro
TmicroA = minusF5ǫ
microναβεlowastνpKlowastαqβ + iF6εlowastmicro + iF7ε
lowast middot q(pB + pKlowast)micro + iF8εlowast middot qqmicro
TS = iF9εlowast middot q
TP = iF10εlowast middot pB
TmicroνT = CT
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
TmicroνE = CTE
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
(32)
The auxiliary functions F1 middot middot middot F13 appearing in eq (32) are defined as follows
F1 =
[
2V (q2)
mB +mKlowast
(Ceff9 +RV +Rprime
V ) +4mb
q2Ceff7 T1(q
2)
]
F2 = minus[
(mB +mKlowast)A1(q2)(Ceff
9 +RV minusRprimeV ) +
2mb
q2Ceff7 T1(q
2)(m2B minusmKlowast)
]
F3 =
[
A(q2)
mB +mKlowast
(Ceff9 +RV minusRprime
V ) +2mb
q2Ceff7
(
T1(q2) +
q2T3(q2)
m2B minusmKlowast
)]
F4 =
[
2mKlowast
q2(Ceff
9 +RV minusRprimeV )(A3(q
2)minusA0(q2))minus 2mb
q2Ceff7 T3(q
2)
]
F5 =
[
2V (q2)
mB +mKlowast
(Ceff10 +RA +Rprime
A)
]
F6 = minus[
(mB +mKlowast)A1(q2)(Ceff
10 +RA minusRprimeA)
]
F7 =
[
A(q2)
mB +mKlowast
(Ceff10 +RA minusRprime
A)
]
F8 =
[
2mKlowast
q2(Ceff
10 +RA minusRprimeA)(A3(q
2)minusA0(q2))
]
F9 =
[
minus2(RS minusRprimeS)
mKlowast
mbA0(q
2)
]
ndash 8 ndash
JHEP02(2012)045
F10 =
[
2(RP minusRprimeP )
mKlowast
mbA0(q
2)
]
F11 = minus2T1(q2)
F12 =
[
2(m2B minusm2
Klowast)
q2(T1(q
2)minus T2(q2))
]
F13 =
[
4
q2
(
T1(q2)minus T2(q
2)minus q2T3(q2)
m2B minusm2
Klowast
)]
(33)
31 Differential decay rate
The differential decay width of B rarr Klowast2 (1430)micro
+microminus in dilepton center of mass frame can
be written as
dΓ(B rarr Klowast2 (1430)micro
+microminus)
dq2=
1
(2π)31
32m3B
int u(q2)
minusu(q2)|MBrarrKlowast
2(1430)micro+microminus |2du (34)
where u = (p + pmicrominus)2 minus (p + pmicro+)2 = u(q2) cos θ and q2 = (pmicro+ + pmicrominus)2 p k pmicro+ and
pmicrominus are the four-momenta vectors of B Klowast2 (1430) micro
+ and microminus respectively and u(q2) are
given by
u(q2) =radic
m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2
radic
1minus 4m2l
q2(35)
Collecting everything together one can write the general expression of the differential decay
rate for B rarr Klowast2 (1430)micro
+microminus as
dΓ
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
18m2lm
4T q
2
3F21m
2Klowast
2q2λ+ 2F2
2m4B(λ+ 10m2
T q2) (36)
+2F23λ
2] (
2m2l + q2
)
minus[
3F25m
2Klowast
2minus 3F2
9m2B
]
K2q2λ+ 12F2
8m2l q
4λ
+2F26m
4B
[
2(
λminus 20m2T q
2)
m2l + q2
(
λ+ 10m2T q
2)]
+ 3F210m
2Bq
4λ
+2F27λ
[
2(
λminus 3q4 + 6m2T q
2)
m2Klowast
2+ q2λ
]
minus 4F2F3m4B
(
2m2l + q2
)
K1λ2
minus4F6F7m2Bλ
[
2(
K1 + 3q2)
m2l +K1q
2]
minus 24F6F8m2lm
2Bq
2λminus 12F10F6mlm3Bq
2λ
+24F7F8m2lK0q
2λ+ 12F10F7mlmBK0q2λ+ 8F11F12q
2(λ+ 10m2Tm
2B minus 10m4
T )K3
minus4F11F13(K1 + 4m2T )λq
2K3 minus 72F1F11mlm2Klowast
2q2λCT
+48F11F2mlm2Bq
2(λ+ 10m2Tm
2B minus 10m4
T )CTE minus 4F12F13K1λq2K3
+48F12F2mlm2Bq
2(
λ+ 10m2T q
2)
CTE minus 48F12F3mlq2K1CTEλ
minus24F13F2mlm2BK1λq
2CTE + 24F13F3mlq2CTEλ
2
where ml is the mass of final state muon and
λ = λ(
m2Bm
2Klowast
2 q2
)
equiv m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2 (37)
K0 = (m2B minusm2
Klowast
2) K1 =
(
m2B minusm2
Klowast
2minus q2
)
K2 = q2 minus 4m2l
K3 = q2C2T minus 4m2
l
(
C2T minus 36C2
TE
)
(38)
and the auxiliary functions are the same as defined in eq (33)
ndash 9 ndash
JHEP02(2012)045
32 Forward-backward asymmetry
Now we are in a position to explore the forward-backward asymmetry of final state leptons
in the B rarr Klowast2 (1430)micro
+microminus which is an essential observable sensitive to the new physics
effects To calculate the forward-backward asymmetry we consider the following double
differential decay rate formula for the process B rarr Klowast2 (1430)micro
+microminus
d2Γ(q2 cos θ)
dq2d cos θ=
1
(2π)31
64m3B
u(q2)|MBrarrKlowast
2(1430)micro+microminus |2 (39)
where θ is the angle between the momentum of B baryon and lminus in the dilepton rest frame
The differential and normalized FBAs for the semi-leptonic decay B rarr Klowast2 (1430)l
+lminus are
defined as
dAFB(q2)
dq2=
int 1
0d cos θ
d2Γ(q2 cos θ)
dq2d cos θminusint 0
minus1d cos θ
d2Γ(q2 cos θ)
dq2d cos θ(310)
and
AFB(q2) =
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θminusint 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θ+int 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
(311)
Following the same procedure as we did for the differential decay rate one can easily get
the expression for the forward-backward asymmetry as follows
dAFB(q2)
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
6mBm4T
[
AV AFB +ASP
FB +ATSPFB +AT
FB
]
(312a)
AV AFB = minus3(F2F5 + F1F6)q
2m2Bm
2K2
(312b)
ASPFB = 2F9mlmB
(
F3λ+ F2m2B
[
q2 minusm2B +m2
K2
])
(312c)
ATSPFB = minusq2 (F10CT + 2F9CTE)mB
(
2F12
(
m2B minusm2
K2minus q2
)
(312d)
minusF13λ+ 2F11
(
m2B + 3m2
K2minus q2
))
ATFB = minus2ml
(
12F12F5q2CTEm
2K2
+ 12F11F5CTEm2K2
(
m2B minusm2
K2
)
(312e)
+F13λCT
(
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F12CT
(
m2B minusm2
K2minus q2
) (
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F11CT
(
F6m2B
(
m2B + 9m2
K2minus q2
)
minus(
m2B + 3m2
K2minus q2
) (
F8q2 + F7
(
m2B minusm2
K2
)))
and the expression of the differential decay rate is given in eq (36)
33 Lepton polarization asymmetries
In the rest frame of the lepton microminus the unit vectors along longitudinal normal and transver-
sal component of the microminus can be defined as [55]
sminusmicroL = (0 ~eL) =
(
0~pminus|~pminus|
)
sminusmicroN = (0 ~eN ) =
0~k times ~pminus∣
∣
∣
~k times ~pminus∣
∣
∣
(313)
sminusmicroT = (0 ~eT ) = (0 ~eN times ~eL)
ndash 10 ndash
JHEP02(2012)045
where ~pminus and ~k are the three-momenta of the microminus and Klowast2 (1430) meson respectively in the
center mass (CM) frame of micro+microminus system Lorentz transformation is used to boost the
longitudinal component of the lepton polarization to the CM frame of the lepton pair as
(
sminusmicroL
)
CM=
( |~pminus|ml
El~pminusml |~pminus|
)
(314)
where El and ml are the energy and mass of the final state muon The normal and
transverse components remain unchanged under the Lorentz boost The longitudinal (PL)
normal (PN ) and transverse (PT ) polarizations of lepton can be defined as
P(∓)i (q2) =
dΓdq2
(~ξ∓ = ~e∓)minus dΓdq2
(~ξ∓ = minus~e∓)dΓdq2
(~ξ∓ = ~e∓) + dΓdq2
(~ξ∓ = minus~e∓)(315)
where i = L N T and ~ξ∓ is the spin direction along the leptons micro∓ The differential
decay rate for polarized lepton l∓ in B rarr Klowast2 (1430)micro
+microminus decay along any spin direction~ξ∓ is related to the unpolarized decay rate (36) with the following relation
dΓ(~ξ∓)
dq2=
1
2
(
dΓ
dq2
)
[1 + (P∓L ~e∓L + P∓
N~e∓N + P∓T ~e∓T ) middot ~ξ∓] (316)
We can achieve the expressions of longitudinal normal and transverse polarizations for
B rarr Klowast2 (1430)micro
+microminus decays as collected below The longitudinal lepton polarization can
be written as
PL prop1
36m2Bm
4T
4u(q2)radicλ[
P V AL + PSP
L + P TL
]
(317a)
P V AL = ml
(
2λF2 (F6 minusF7)m4B +
(
3λF1F5q2 + 2F2m
2B
(
10q2F6m2B + λF7
))
m2Klowast
2
+2λF3
(
F6
(
q2 minusm2B +m2
Klowast
2
)
m2B + λF7
))
(317b)
PSPL = 3mlλF9mB
(
minus2mlF8q2 minusF10mBq
2 + 2ml
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
(317c)
P TL = m2
lF11
(
24 (CTEF1 minus CTF5)m2Klowast
2λ+ 4CTλF3
(
m2B + 3m2
Klowast
2minus q2
)
+4m2B (4CTEF6 minus CTF2)
(
10(
m2B minusm2
Klowast
2
)
m2Klowast
2+ λ
))
+m2lF12
(
4m2B (4CTEF6 minus CTF2)
(
10q2m2Klowast
2+ λ
)
minus 4CTF3
(
q2 minusm2B +m2
Klowast
2
))
+m2lF13
(
2CTλminus 4CTF2m2B
(
m2B minusm2
Klowast
2minus q2
)
minus 2CTλ2F3
)
(317d)
ndash 11 ndash
JHEP02(2012)045
Similarly the normal lepton polarization is
PN prop minusπu(q2)t
(12m2Bm
4T
(λ
t)32
[
P V AN + PSP
N + P TN
]
(318a)
P V AN = 2ml
(
F2
(
F8q4 minus
(
(F6 minusF7 + F8)m2B + (minus3F1 + F7 minusF8)m
2Klowast
2
)
q2 (318b)
+(
m2B minusm2
Klowast
2
)
m2B
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
+ λF3
(
F8q2 minusF6m
2B + F7
(
m2B minusm2
Klowast
2
)))
PSPN = mBλ
(
F3F10q2 +
(
q2 minus 4m2l
)
F7F9
)
(318c)
minus(
F2F10q2 +
(
q2 minus 4m2l
)
F6F9
)
m3B
(
m2B minusm2
Klowast
2minus q2
)
P TN = F13
(
8m2l λCTE
(
F8q2 minusF6m
2B minusF7
(
m2Klowast
2minusm2
B
))
+ 4mlmBλCTEF10q2)
+F12
(
16m2lCTE
(
F6m2BminusF7
(
m2Bminusm2
Klowast
2
)
minusF8q2minusmB
2mlF10q
2
)
(
m2Bminusm2
Klowast
2minusq2
)
+ 6(
4m2l + q2
)
CTEF1q2m2
Klowast
2+ 3
(
q2 minus 4m2)
CTF5q2m2
Klowast
2
)
+F11
(
minus16m2lCTE
(
F8q2 + F7
(
m2B minusm2
Klowast
2
)
+mB
2mlF10q
2
)
(
m2B + 3m2
Klowast
2minus q2
)
+6m2Klowast
2
(
4m2l + q2
)
(
CTEF1
(
m2B minusm2
Klowast
2
)
minus CTF2m2B
)
+3(
4m2l minus q2
)
CTF5m2Klowast
2
(
m2Klowast
2minusm2
B
)
+4CTEF6m2B
(
4m2l
(
m2B + 6m2
Klowast
2minus q2
)
minus 3q2m2Klowast
2
)
)
(318d)
and the transverse one is given by
PT propiπλq2u(q2)
12mBm2Klowast
2
λCTEF13
(
4F2m2B minus 3F5m
2Klowast
2+ F3
(
q2 minus 5m2B +m2
Klowast
2
))
(319)
minus2F12
(
2CTE
((
8F3m2B minus (2F3 + 3F5)m
2Klowast
2
)
q2 + 4F2m2B
(
2m2B +m2
Klowast
2minus 2q2
)
minus(
m2Bminusm2
Klowast
2
)(
8F3m2B + (4F3 + 3F5)m
2Klowast
2
))
minus3CTF1m2Klowast
2
(
q2minus3m2B + 3m2
Klowast
2
))
+2F11
(
2CTE
(
3F5m2Klowast
2
(
3m2B +m2
Klowast
2minus q2
)
minus 4F2
(
2m2B + 3m2
Klowast
2minus 2q2
)
m2B
+2F3
(
7m2Klowast
2q2minus4q4+6λ+4m2
B
(
q2+5m2Klowast
2
)))
minus3CTF1m2Klowast
2
(
3m2B+m2
Klowast
2minusq2
)
34 Helicity fractions
Helicity fraction is an observable associated with polarization of the out going meson that
is almost free of hadronic uncertainties The spin-2 polarization tensor which satisfies
ǫmicroνkν = 0 with k being the momentum is symmetric and traceless It can be constructed
by the vector polarization ǫmicro as
ǫmicroν(plusmn2) = ǫmicro(plusmn)ǫν(plusmn) ǫmicroν(plusmn1) =1radic2[ǫmicro(plusmn)ǫν(0) + ǫmicro(0)ǫν(plusmn)]
ǫmicroν(0) =1radic6[ǫmicro(+)ǫν(minus) + ǫmicro(minus)ǫν(+)] +
radic
2
3ǫmicro(0)ǫν(0) (320)
ndash 12 ndash
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
Contents
1 Introduction 1
2 B rarr Klowast
2(1430)micro+microminus operators and matrix elements 3
21 Standard model 3
22 New physics operators 4
23 Parametrization of matrix elements and form factors 5
24 Numerical constraints on NP parameters 6
3 Decay rate forward-backward asymmetry and lepton polarization a-
symmetries for B rarr Klowast
2(1430)micro+microminus decay 8
31 Differential decay rate 9
32 Forward-backward asymmetry 10
33 Lepton polarization asymmetries 10
34 Helicity fractions 12
4 Numerical Analysis 13
41 V A new-physics operators 15
42 SP new-physics operators 20
43 T operators and interference of SP and T operators 22
44 All NP operators together 26
5 Conclusions 30
1 Introduction
The wealthy data taken from the Tevatron experiments on Bs and the other B-factories
have reached to the luminosity where billions of B mesons will be produced which will help
us to enter into the precision era of B physics The Standard Model (SM) is enormously
successful in explaining most of the data to date However some discrepancies in the
predication of the SM have been observed in B decays [1ndash4] The pertinent examples are
(i) in B rarr Kπ decays it is difficult to account for all the experimental measurements of
CP asymmetry in neutral and charged modes within the SM [7] (ii) the B0s minus B0
s mixing
phase by the CDF and DO collaboration deviates from the SM prediction [5 6] (iii) the
isospin asymmetry between neutral and the charged decay modes of the B rarr Klowastℓ+ℓminus
decay also deviate from the SM [8 9] The Large Hadron Collider (LHC) is already up
and running where CMS ATLAS and LHCb have already started taking data while the
Super-B factories are on their way Therefore it is an ideal time to test the predictions of
SM and try to identify the nature of physics that is beyond SM
ndash 1 ndash
JHEP02(2012)045
In SM the zero crossing of the AFB(q2) in B rarr Klowastl+lminus is at a well determined
position which is free from the hadronic certainties at the leading order (LO) in strong
coupling αs [11ndash13] Recently the LHCb has announced the results of AFB for the decay
B rarr Klowastmicro+microminus that are close to the SM predictions They have collected over 300 events
for this decay with signal to background ratio above 3 which is the largest sample of such
decays in the world and is even cleaner than the sample used by the B factories These
results of AFB(B rarr Klowastmicro+microminus) are close to the SM predictions with slight error bars thus
they have overwritten the earlier measurements by Belle with better statistics [15] The
collaboration plans to continue to study the channel B rarr Klowastmicro+microminus in finer detail with
measurements that include more angular variables and expected to achieve high sensitivity
to any small deviation from the SM [15]
In order to incorporate the experimental predictions of different physical observables
in B rarr Klowastmicro+microminus this decay has been studied in SM and in number of different NP scenar-
ios [10 12 16ndash36] where NP effects display themselves through modification in the Wilson
coefficients as well as through the new operators Beside these models the general analysis
of B rarr Klowastmicro+microminus decay has also been performed which allow us to include all possible
NP effects like vector-axial vector (V A) scalar-pseudoscalar (SP ) and tensor-axial tensor
(TE) [37] This study has shown that the interference of V A operators among themselves
and with the SM operators is the cause of the larger magnitude of AFB(q2) as well as the
shift in the zero position of the AFB(q2) In addition to this it is also pointed out that the
SP and T operators not only influence the AFB(q2) but also give viable effects in other
physical observables
In general there are two ways to search NP which are considered to resolve anomalies
in the experimental measurements One is the direct search which can be achieved by
increasing the energies of colliders and find the predicted new particles but these particles
are quite massive and therefore hard to produced The other one is indirect search which
is comparatively easier ie to see how much different observables are affected by these new
particles The indirect searches require precise measurement of the observables for the
channel under consideration as well as need rigorous complementary studies
It is therefore indispensable to study the impact of NP on the different observables for
the decay channels other than the B rarr Klowastmicro+microminus With this motivation the B rarr Klowast2ℓ
+ℓminus
channel where Klowast2 is the excited state of Klowast with parity 2+ provide the same testing
ground to study the effects of the NP as B rarr Klowastmicro+microminus decay The exclusive B rarrKlowast
2 (1430)ℓ+ℓminus decay has been studied in the SM and some approaches beyond SM [38ndash46]
For example in refs [38 39] the form factors for B rarr Klowast2ℓ
+ℓminus are calculated using pertur-
bative QCD and LCSR approaches The analysis of different physical observable for this
decay is studied in various beyond SM scenarios like SM4 non-universal Z prime model Uni-
versal Extra dimension model and a model with the flipped sign of Ceff7 has been performed
in [40ndash42 45] The analysis of lepton polarization asymmetries of B rarr Klowast2ℓ
+ℓminus in the pres-
ence of new right-handed currents is done in [43 44] The analysis of polarized decay width
and forward-backward asymmetry by considering beyond SM operator basis is given in [46]
These studies show that like B rarr Klowastℓ+ℓminus decay this channel is also quite promising in
finding NP and will provide us some independent tests of the physics of the SM and beyond
ndash 2 ndash
JHEP02(2012)045
In this paper we will perform the study of B rarr Klowast2 (1430)micro
+microminus on the lines of ref [37]
and study the NP effects without restricting ourselves to any specific model Contrary to
B rarr Klowastmicro+microminus the decay B rarr Klowast2 (1430)micro
+microminus is not yet experimentally observed We have
taken into account the constraints from the different B decay mode such as Bs rarr micro+microminus
B rarr Xsmicro+microminus and B rarr Klowastmicro+microminus on different NP operator couplings allowed by the
most general lorentz structure of transition matrix elements In this paper we will also
incorporate bounds on the input parameters coming from the recent AFB measurements
at LHCb experiment for the decay B rarr Klowast(892)micro+microminus [15] With these new bounds we
will obtain better understanding of how these new physics operators affect branching ratio
zero-position of forward-backward asymmetry different lepton polarization asymmetries
and the helicity fractions of final state meson
The effects of these new operators couplings (VASPT) are significant to the zero
position of AFB(q2) as well as on its magnitude In addition to AFB these NP operators
also give significant effects on decay rate lepton polarization asymmetries and longitudinal
and transverse helicities of final state Klowast2 (1430) meson We hope that in the coming years
the LHCb experiment will collect around 64k events in the full range of q2 for an integrated
luminosity of 2fbminus1 [37] This would allow us to observe the B rarr Klowast2 (1430)micro
+microminus in the
SM and would also permit many of the additional tests of NP
The paper is organized as follows in section 2 the necessary hadronic inputs namely
basic Hamiltonian and form factors and constraints on the NP parameters are collected
Section 3 contains the analytic formulas for differential decay rates forward backward
asymmetry different polarizations (longitudinal normal and transverse) and the helicity
fractions of the final state Klowast2 (1430) meson Section 4 deals with the numerical analysis
and then conclusions are summarized in section 5
2 B rarr Klowast
2(1430)micro+microminus operators and matrix elements
21 Standard model
The semileptonic decay mode B rarr Klowast2 (1430)l
+lminus where l = micro for our case is governed
by the quark level transitions b rarr sl+lminus In SM the effective Hamiltonian corresponding
to this transition is given by
HSMeff = minus4GFradic
2V lowasttbVts
10sum
i=1
Ci(micro)Oi(micro) (21)
where Oi(micro)(i = 1 10) are four quark operators and Ci(micro) are the corresponding Wilson
coefficients Out of these 10 operators the O7 O9 and O10 are the relevant for B rarrKlowast
2 (1430)l+lminus decay and these can be written as
O7 =e
16π2[sσmicroν (msPL +mbPR) b]F
microν
O9 =e
16π2[sγmicroPLb]
(
lγmicrol)
O10 =e
16π2[sγmicroPLb]
(
lγmicroγ5l)
(22)
with PLR = (1plusmn γ5) 2
ndash 3 ndash
JHEP02(2012)045
In term of these operators the effective Hamiltonian for B rarr Klowast2 (1430)l
+lminus takes the
form
HSMeff = minusGFαradic
2πVtbV
lowastts
CSM9 (sγmicroPLb)(lγ
microl) + CSM10 (sγmicroPLb)(lγ
microγ5l)
minus2mbCSM7 (siσmicroν
qν
q2PRb)(lγ
microl)
(23)
where q2 is square of the sum of the momentum of final state leptons At the scale micro =
48GeV the SM Wilson coefficients takes the following values which are calculated at next-
to-next-to-leading order
Ceff7 = minus034 Ceff
9 = 4211 + Y (q2) C10 = minus4103 (24)
where Ceff7 = C7 minus C33minus 4C49minus 20C53minus 80C69 The function Y (q2) is given by
Y (z q2) = h(z q2)(3C1(micro) + C2(micro) + 3C3(micro) + C4(micro) + 3C5(micro) + C6(micro))
minus1
2h(1 sprime)(4C3(micro) + 4C4(micro) + 3C5(micro) + C6(micro))
minus1
2h(0 q2)(C3(micro) + 3C4(micro)) +
2
9(3C3(micro) + C4(micro) + 3C5(micro) + C6(micro)) (25)
with
h(z q2) = minus8
9lnz +
8
27+
4
9xminus 2
9(2 + x)|1minus x|12
ln∣
∣
∣
radic1minusx+1radic1minusxminus1
∣
∣
∣minus iπ for x equiv 4z2q2 lt 1
2 arctan 1radicxminus1
for x equiv 4z2q2 gt 1
h(0 q2) =8
27minus 8
9lnmb
microminus 4
9lnq2 +
4
9iπ (26)
and z = mcmb
22 New physics operators
The NP effects in semileptonic B meson decays can be established in two ways in one case
we can change the Wilson Coefficients but leave the operator basis same as that of the SM
and in other case we can add new operators too Here we do not restrict ourself to any
model and discuss all possible operators that corresponds to B rarr Klowast2 (1430)l
+lminus decays
In this scenario the total effective Hamiltonian for brarr sl+lminus can be written as
Heff = HSMeff +HV A
eff +HSPeff +HT
eff (27)
where HSMeff is given in eq (23) while [37]
HV Aeff =minus 4GFradic
2
α
4πV lowasttsVtb RV (sγmicroPLb) microγmicromicro+RA (sγmicroPLb) microγmicroγ5micro
+RprimeV (sγmicroPRb) microγmicromicro+Rprime
A (sγmicroPRb) microγmicroγ5micro
(28)
HSPeff =minus 4GFradic
2
α
4πV lowasttsVtb RS (sPRb) micromicro+RP (sPRb) microγ5micro
+RprimeS (sPLb) micromicro+Rprime
P (sPLb) microγ5micro
(29)
HTeff =minus 4GFradic
2
α
4πV lowasttsVtb
CT (sσmicroνb) microσmicroνmicro+ iCTE (sσmicroνb) microσαβmicroǫmicroναβ
(210)
ndash 4 ndash
JHEP02(2012)045
Here RV RA RV RprimeA RS RP R
primeS R
primeP CT and CTE are the NP effective couplings The
constraints on the numerical values of these NP coupling from different B meson decays
will be given later in this section
23 Parametrization of matrix elements and form factors
The exclusive B rarr Klowast2 (1430)l
+lminus decay involves the hadronic matrix elements of quark
operators which can be parameterized in terms of form factors These form factors are
written as
lang
Klowast2 (k ǫ) |sγmicrob|B(p)
rang
= minus 2V (q2)
mB +mKlowast
2
ǫmicroνρσεlowastναp
α
mBpρkσ (211)
lang
Klowast2 (k ǫ)
∣
∣sγmicroγ5b∣
∣B(p)rang
=2imKlowast
2A0(q
2)
q2εlowastναp
α
mBqνqmicro
+i(mB +mKlowast
2)A1(q
2)
mB
[
gmicroνεlowastναpα minus 1
q2εlowastναp
αqνqmicro]
minusiA2(q2)
εlowastναpαqν
mB(mB +mKlowast
2)
[
(pmicro + kmicro)minusm2
B minusm2Klowast
2
q2qmicro
]
(212)lang
Klowast2 (k ǫ) |sσmicroνqνb|B(p)
rang
= minus2iT1(q2)ǫmicroνρσ
εlowastναpα
mBpρkσ (213)
lang
Klowast2 (k ǫ)
∣
∣sσmicroνγ5qνb∣
∣B(p)rang
= T2(q2)[
(m2B minusm2
Klowast
2)gmicroνεlowastναp
α minus εlowastναpαqν(pmicro + kmicro)
] 1
mB
+T3(q2)εlowastναp
α
mBqν
[
qmicro minus q2
m2B minusm2
Klowast
2
(pmicro + kmicro)
]
(214)
lang
Klowast2 (k ǫ) |sb|B(p)
rang
=2V (q2)
(mB +mKlowast
2)(mb minusms)
ǫmicroνρσεlowastναp
α
mBpρkσ (215)
lang
Klowast2 (k ǫ)
∣
∣sγ5b∣
∣ B(p)rang
=2imKlowast
2A0(q
2)
q2εlowastναp
α
mB(mb +ms)qνqmicro (216)
lang
Klowast2 (k ǫ) |sσmicroνb|B(p)
rang
= minus2T1(q2)ǫmicroνρσ
εlowastναpα
mBpρkσ (217)
where p(k) is the momentum of the B(Klowast2 ) meson and εlowastνα is the polarization of the final
state Klowast2 (1430) meson In case of the tensor meson the polarization sum is given by [38]
Pmicroναβ =sum
εmicroν(p)εlowastαβ(p) =
1
2(θmicroαθνβ + θmicroβθνα)minus
1
3(θmicroνθαβ) (218)
with
θmicroν = minusgmicroν +kmicrokνm2
Klowast
2
(219)
Defining
εlowastν = εlowastναpαmB (220)
the resulting matrix elements for B rarr Klowast2 (1430) will look just like the B rarr V (eg Klowast
meson) transitions The form factors for B rarr Klowast2 (1430) transition are the non-perturbative
ndash 5 ndash
JHEP02(2012)045
F (q2) F (0) a b
V (q2) 016+002minus002 208 15
A0(q2) 025+004
minus004 157 01
A1(q2) 014+002
minus002 123 049
A2(q2) 005+002
minus002 132 149
T1(q2) 014+002
minus002 207 15
T2(q2) 014+002
minus002 122 034
T3(q2) 001+001
minus002 991 276
Table 1 B rarr Klowast
2 form factors in the light cone sum rules approach F (0) denotes the value
of form factors at q2 = 0 while a and b are the parameters in the parameterizations shown in
eq (221) [39]
quantities and are needed to be calculated using different approaches (both perturbative
and non-perturbative) like Lattice QCD QCD sum rules Light Cone sum rules etc Here
we will consider the form factors calculated in the LCSR approach [39] and their evolution
with q2 is given by
F (q2) =F (0)
1minus a(q2m2B) + b(q2m2
B)2
(221)
where the value of different parameters is given in table 1
The errors in the values of the form factors arise from number of input parameters
involved in their calculation in LCSR such as variations in the Boral parameters fluctuation
of threshold parameters errors in the b quark mass corrections from the decay constants
of involved mesons and from the Gengenbauer moments in the distribution amplitudes
It is worth mentioning here that it is possible to study this mode with the help of
QCD factorization which might discover additional sources of theoretical errors which are
overlooked in the simple form factor analysis As besides the factorizable contribution of
form factors which has been used here there are in principle non-factorizable contributions
to matrix elements as well [13] QCD factorization not only reduce the number of inde-
pendent parameters in heavy quark limit but also help us to compute the non-factorizable
corrections to B meson decays with the help of light-cone distribution amplitudes and
hard scattering kernel [53 54] The details of QCD factorization and its implications in
semileptonic and radiative B meson decays can be found in [13]
24 Numerical constraints on NP parameters
The constraints on NP parameters can be obtained from the branching ratios of B0s rarr
micro+microminus B0s rarr Xsmicro
+microminus and B0d rarr Kmicro+microminus [5 47ndash50] Due to the large hadronic uncertain-
ties the constraints obtained from the exclusive decay modes are somewhat weaker com-
pared to the inclusive ones The branching ratio of inclusive decay mode B rarr Xsmicro+microminus has
been measured by Babar [49] and Belle [50] and their measurements in low-q2 (1GeV2 le
ndash 6 ndash
JHEP02(2012)045
q2 le 6GeV2) and high-q2 (144GeV2 le q2 le 25GeV2) regions can be summarized as
B(B rarr Xsmicro+microminus)low q2 = (149plusmn 050+041
minus032)times 10minus6 (Belle)
(18plusmn 07plusmn 050)times 10minus6 (BaBar) (222)
(160plusmn 050)times 10minus6 (Average)
B(B rarr Xsmicro+microminus)high q2 = (042plusmn 012+007
minus007)times 10minus6 (Belle)
(050plusmn 025+007minus008)times 10minus6 (BaBar) (223)
(044plusmn 012)times 10minus6 (Average)
where q2 is the invariant mass squared of two muons and low-q2 region corresponds to
1GeV2 le q2 le 6GeV2 and high-q2 region corresponds to q2 ge 144GeV2
The constraints on the new V A couplings come mainly from B0d rarr Xsmicro
+microminus and B0d rarr
Kmicro+microminus [51] It has been shown in ref [51] that if RVA couplings are present only the
constraints on these couplings from above said decays came to be
10 le |RV + 36|2(47)2
+|RA minus 40|2
(48)2|RV + 28|2
(65)2+|RA minus 41|2
(66)2le 1 (224)
Similarly when we have only RprimeVA couplings the constraints on them from the same decay
will become [51]
22 le |RprimeV + 36|2 + |Rprime
A minus 40|2 le 566 |RprimeV |2 + |Rprime
A|2 le 17 (225)
These constraints are weekend when both RVA and RprimeVA couplings are present at the same
time In this case these new physics couplings are restricted to be
|RV + 28|2(65)2
+|RA minus 41|2
(66)2le 1 (226)
and
|RprimeV |2 + |Rprime
A|2 le 40 (227)
The limits on couplings corresponding to scalar-pseudoscalar (SP) operators comes
from the upper bound on B0s rarr micro+microminus which provides the limit
|RS minusRprimeS |2 + |RP minusRprime
P |2 le 044 (228)
This puts a sever constraint on the NP couplings if only RSP or RprimeSP are present However
under the condition where both types of operators are present RSP or RprimeSP these bounds
can be relaxed due to cancelation between the RSP and RprimeSP In this case B0
d rarr Xsmicro+microminus
and B0d rarr Kmicro+microminus can still bound these couplings and the stronger bound is obtained from
the measurement of later quantity which yields
|RS |2 + |RP |2 le 9 RS asymp RprimeS RS asymp Rprime
P (229)
Now the constraint on the NP tensor type couplings comes entirely from the inclusive
B0d rarr Xsmicro
+microminus decay In case when only tensor type operators are present the limits on
tensor type couplings are [51]
|CT |2 + |CTE |2 le 10 (230)
ndash 7 ndash
JHEP02(2012)045
In the present study we will examine B rarr Klowast2 (1430)micro
+microminus decays by using these NP
constraints
3 Decay rate forward-backward asymmetry and lepton polarization a-
symmetries for B rarr Klowast
2(1430)micro+microminus decay
In this section we are going to perform the calculations of some very interesting quantities
like the decay rate the forward-backward asymmetry the polarization asymmetries of
the final state lepton and the helicity fractions of the final state Klowast2 (1430) meson From
eq (27) it is straightforward to obtain the decay amplitude for B rarr Klowast2 (1430)micro
+microminus as
M(B rarr Klowast2 (1430)micro
+microminus) = minus GFα
2radic2π
VtbVlowastts
[
TmicroV lγmicrol + Tmicro
A lγmicroγ5l
+TS ll + TP lγ5l + Tmicroν
T lσmicroν l + iTmicroνE ǫmicroναβ lσαβl
]
(31)
with
TmicroV = minusF1ǫ
microναβεlowastνpKlowastαqβ + iF2εlowastmicro + iF3ε
lowast middot q(pB + pKlowast)micro + iF4εlowast middot qqmicro
TmicroA = minusF5ǫ
microναβεlowastνpKlowastαqβ + iF6εlowastmicro + iF7ε
lowast middot q(pB + pKlowast)micro + iF8εlowast middot qqmicro
TS = iF9εlowast middot q
TP = iF10εlowast middot pB
TmicroνT = CT
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
TmicroνE = CTE
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
(32)
The auxiliary functions F1 middot middot middot F13 appearing in eq (32) are defined as follows
F1 =
[
2V (q2)
mB +mKlowast
(Ceff9 +RV +Rprime
V ) +4mb
q2Ceff7 T1(q
2)
]
F2 = minus[
(mB +mKlowast)A1(q2)(Ceff
9 +RV minusRprimeV ) +
2mb
q2Ceff7 T1(q
2)(m2B minusmKlowast)
]
F3 =
[
A(q2)
mB +mKlowast
(Ceff9 +RV minusRprime
V ) +2mb
q2Ceff7
(
T1(q2) +
q2T3(q2)
m2B minusmKlowast
)]
F4 =
[
2mKlowast
q2(Ceff
9 +RV minusRprimeV )(A3(q
2)minusA0(q2))minus 2mb
q2Ceff7 T3(q
2)
]
F5 =
[
2V (q2)
mB +mKlowast
(Ceff10 +RA +Rprime
A)
]
F6 = minus[
(mB +mKlowast)A1(q2)(Ceff
10 +RA minusRprimeA)
]
F7 =
[
A(q2)
mB +mKlowast
(Ceff10 +RA minusRprime
A)
]
F8 =
[
2mKlowast
q2(Ceff
10 +RA minusRprimeA)(A3(q
2)minusA0(q2))
]
F9 =
[
minus2(RS minusRprimeS)
mKlowast
mbA0(q
2)
]
ndash 8 ndash
JHEP02(2012)045
F10 =
[
2(RP minusRprimeP )
mKlowast
mbA0(q
2)
]
F11 = minus2T1(q2)
F12 =
[
2(m2B minusm2
Klowast)
q2(T1(q
2)minus T2(q2))
]
F13 =
[
4
q2
(
T1(q2)minus T2(q
2)minus q2T3(q2)
m2B minusm2
Klowast
)]
(33)
31 Differential decay rate
The differential decay width of B rarr Klowast2 (1430)micro
+microminus in dilepton center of mass frame can
be written as
dΓ(B rarr Klowast2 (1430)micro
+microminus)
dq2=
1
(2π)31
32m3B
int u(q2)
minusu(q2)|MBrarrKlowast
2(1430)micro+microminus |2du (34)
where u = (p + pmicrominus)2 minus (p + pmicro+)2 = u(q2) cos θ and q2 = (pmicro+ + pmicrominus)2 p k pmicro+ and
pmicrominus are the four-momenta vectors of B Klowast2 (1430) micro
+ and microminus respectively and u(q2) are
given by
u(q2) =radic
m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2
radic
1minus 4m2l
q2(35)
Collecting everything together one can write the general expression of the differential decay
rate for B rarr Klowast2 (1430)micro
+microminus as
dΓ
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
18m2lm
4T q
2
3F21m
2Klowast
2q2λ+ 2F2
2m4B(λ+ 10m2
T q2) (36)
+2F23λ
2] (
2m2l + q2
)
minus[
3F25m
2Klowast
2minus 3F2
9m2B
]
K2q2λ+ 12F2
8m2l q
4λ
+2F26m
4B
[
2(
λminus 20m2T q
2)
m2l + q2
(
λ+ 10m2T q
2)]
+ 3F210m
2Bq
4λ
+2F27λ
[
2(
λminus 3q4 + 6m2T q
2)
m2Klowast
2+ q2λ
]
minus 4F2F3m4B
(
2m2l + q2
)
K1λ2
minus4F6F7m2Bλ
[
2(
K1 + 3q2)
m2l +K1q
2]
minus 24F6F8m2lm
2Bq
2λminus 12F10F6mlm3Bq
2λ
+24F7F8m2lK0q
2λ+ 12F10F7mlmBK0q2λ+ 8F11F12q
2(λ+ 10m2Tm
2B minus 10m4
T )K3
minus4F11F13(K1 + 4m2T )λq
2K3 minus 72F1F11mlm2Klowast
2q2λCT
+48F11F2mlm2Bq
2(λ+ 10m2Tm
2B minus 10m4
T )CTE minus 4F12F13K1λq2K3
+48F12F2mlm2Bq
2(
λ+ 10m2T q
2)
CTE minus 48F12F3mlq2K1CTEλ
minus24F13F2mlm2BK1λq
2CTE + 24F13F3mlq2CTEλ
2
where ml is the mass of final state muon and
λ = λ(
m2Bm
2Klowast
2 q2
)
equiv m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2 (37)
K0 = (m2B minusm2
Klowast
2) K1 =
(
m2B minusm2
Klowast
2minus q2
)
K2 = q2 minus 4m2l
K3 = q2C2T minus 4m2
l
(
C2T minus 36C2
TE
)
(38)
and the auxiliary functions are the same as defined in eq (33)
ndash 9 ndash
JHEP02(2012)045
32 Forward-backward asymmetry
Now we are in a position to explore the forward-backward asymmetry of final state leptons
in the B rarr Klowast2 (1430)micro
+microminus which is an essential observable sensitive to the new physics
effects To calculate the forward-backward asymmetry we consider the following double
differential decay rate formula for the process B rarr Klowast2 (1430)micro
+microminus
d2Γ(q2 cos θ)
dq2d cos θ=
1
(2π)31
64m3B
u(q2)|MBrarrKlowast
2(1430)micro+microminus |2 (39)
where θ is the angle between the momentum of B baryon and lminus in the dilepton rest frame
The differential and normalized FBAs for the semi-leptonic decay B rarr Klowast2 (1430)l
+lminus are
defined as
dAFB(q2)
dq2=
int 1
0d cos θ
d2Γ(q2 cos θ)
dq2d cos θminusint 0
minus1d cos θ
d2Γ(q2 cos θ)
dq2d cos θ(310)
and
AFB(q2) =
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θminusint 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θ+int 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
(311)
Following the same procedure as we did for the differential decay rate one can easily get
the expression for the forward-backward asymmetry as follows
dAFB(q2)
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
6mBm4T
[
AV AFB +ASP
FB +ATSPFB +AT
FB
]
(312a)
AV AFB = minus3(F2F5 + F1F6)q
2m2Bm
2K2
(312b)
ASPFB = 2F9mlmB
(
F3λ+ F2m2B
[
q2 minusm2B +m2
K2
])
(312c)
ATSPFB = minusq2 (F10CT + 2F9CTE)mB
(
2F12
(
m2B minusm2
K2minus q2
)
(312d)
minusF13λ+ 2F11
(
m2B + 3m2
K2minus q2
))
ATFB = minus2ml
(
12F12F5q2CTEm
2K2
+ 12F11F5CTEm2K2
(
m2B minusm2
K2
)
(312e)
+F13λCT
(
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F12CT
(
m2B minusm2
K2minus q2
) (
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F11CT
(
F6m2B
(
m2B + 9m2
K2minus q2
)
minus(
m2B + 3m2
K2minus q2
) (
F8q2 + F7
(
m2B minusm2
K2
)))
and the expression of the differential decay rate is given in eq (36)
33 Lepton polarization asymmetries
In the rest frame of the lepton microminus the unit vectors along longitudinal normal and transver-
sal component of the microminus can be defined as [55]
sminusmicroL = (0 ~eL) =
(
0~pminus|~pminus|
)
sminusmicroN = (0 ~eN ) =
0~k times ~pminus∣
∣
∣
~k times ~pminus∣
∣
∣
(313)
sminusmicroT = (0 ~eT ) = (0 ~eN times ~eL)
ndash 10 ndash
JHEP02(2012)045
where ~pminus and ~k are the three-momenta of the microminus and Klowast2 (1430) meson respectively in the
center mass (CM) frame of micro+microminus system Lorentz transformation is used to boost the
longitudinal component of the lepton polarization to the CM frame of the lepton pair as
(
sminusmicroL
)
CM=
( |~pminus|ml
El~pminusml |~pminus|
)
(314)
where El and ml are the energy and mass of the final state muon The normal and
transverse components remain unchanged under the Lorentz boost The longitudinal (PL)
normal (PN ) and transverse (PT ) polarizations of lepton can be defined as
P(∓)i (q2) =
dΓdq2
(~ξ∓ = ~e∓)minus dΓdq2
(~ξ∓ = minus~e∓)dΓdq2
(~ξ∓ = ~e∓) + dΓdq2
(~ξ∓ = minus~e∓)(315)
where i = L N T and ~ξ∓ is the spin direction along the leptons micro∓ The differential
decay rate for polarized lepton l∓ in B rarr Klowast2 (1430)micro
+microminus decay along any spin direction~ξ∓ is related to the unpolarized decay rate (36) with the following relation
dΓ(~ξ∓)
dq2=
1
2
(
dΓ
dq2
)
[1 + (P∓L ~e∓L + P∓
N~e∓N + P∓T ~e∓T ) middot ~ξ∓] (316)
We can achieve the expressions of longitudinal normal and transverse polarizations for
B rarr Klowast2 (1430)micro
+microminus decays as collected below The longitudinal lepton polarization can
be written as
PL prop1
36m2Bm
4T
4u(q2)radicλ[
P V AL + PSP
L + P TL
]
(317a)
P V AL = ml
(
2λF2 (F6 minusF7)m4B +
(
3λF1F5q2 + 2F2m
2B
(
10q2F6m2B + λF7
))
m2Klowast
2
+2λF3
(
F6
(
q2 minusm2B +m2
Klowast
2
)
m2B + λF7
))
(317b)
PSPL = 3mlλF9mB
(
minus2mlF8q2 minusF10mBq
2 + 2ml
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
(317c)
P TL = m2
lF11
(
24 (CTEF1 minus CTF5)m2Klowast
2λ+ 4CTλF3
(
m2B + 3m2
Klowast
2minus q2
)
+4m2B (4CTEF6 minus CTF2)
(
10(
m2B minusm2
Klowast
2
)
m2Klowast
2+ λ
))
+m2lF12
(
4m2B (4CTEF6 minus CTF2)
(
10q2m2Klowast
2+ λ
)
minus 4CTF3
(
q2 minusm2B +m2
Klowast
2
))
+m2lF13
(
2CTλminus 4CTF2m2B
(
m2B minusm2
Klowast
2minus q2
)
minus 2CTλ2F3
)
(317d)
ndash 11 ndash
JHEP02(2012)045
Similarly the normal lepton polarization is
PN prop minusπu(q2)t
(12m2Bm
4T
(λ
t)32
[
P V AN + PSP
N + P TN
]
(318a)
P V AN = 2ml
(
F2
(
F8q4 minus
(
(F6 minusF7 + F8)m2B + (minus3F1 + F7 minusF8)m
2Klowast
2
)
q2 (318b)
+(
m2B minusm2
Klowast
2
)
m2B
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
+ λF3
(
F8q2 minusF6m
2B + F7
(
m2B minusm2
Klowast
2
)))
PSPN = mBλ
(
F3F10q2 +
(
q2 minus 4m2l
)
F7F9
)
(318c)
minus(
F2F10q2 +
(
q2 minus 4m2l
)
F6F9
)
m3B
(
m2B minusm2
Klowast
2minus q2
)
P TN = F13
(
8m2l λCTE
(
F8q2 minusF6m
2B minusF7
(
m2Klowast
2minusm2
B
))
+ 4mlmBλCTEF10q2)
+F12
(
16m2lCTE
(
F6m2BminusF7
(
m2Bminusm2
Klowast
2
)
minusF8q2minusmB
2mlF10q
2
)
(
m2Bminusm2
Klowast
2minusq2
)
+ 6(
4m2l + q2
)
CTEF1q2m2
Klowast
2+ 3
(
q2 minus 4m2)
CTF5q2m2
Klowast
2
)
+F11
(
minus16m2lCTE
(
F8q2 + F7
(
m2B minusm2
Klowast
2
)
+mB
2mlF10q
2
)
(
m2B + 3m2
Klowast
2minus q2
)
+6m2Klowast
2
(
4m2l + q2
)
(
CTEF1
(
m2B minusm2
Klowast
2
)
minus CTF2m2B
)
+3(
4m2l minus q2
)
CTF5m2Klowast
2
(
m2Klowast
2minusm2
B
)
+4CTEF6m2B
(
4m2l
(
m2B + 6m2
Klowast
2minus q2
)
minus 3q2m2Klowast
2
)
)
(318d)
and the transverse one is given by
PT propiπλq2u(q2)
12mBm2Klowast
2
λCTEF13
(
4F2m2B minus 3F5m
2Klowast
2+ F3
(
q2 minus 5m2B +m2
Klowast
2
))
(319)
minus2F12
(
2CTE
((
8F3m2B minus (2F3 + 3F5)m
2Klowast
2
)
q2 + 4F2m2B
(
2m2B +m2
Klowast
2minus 2q2
)
minus(
m2Bminusm2
Klowast
2
)(
8F3m2B + (4F3 + 3F5)m
2Klowast
2
))
minus3CTF1m2Klowast
2
(
q2minus3m2B + 3m2
Klowast
2
))
+2F11
(
2CTE
(
3F5m2Klowast
2
(
3m2B +m2
Klowast
2minus q2
)
minus 4F2
(
2m2B + 3m2
Klowast
2minus 2q2
)
m2B
+2F3
(
7m2Klowast
2q2minus4q4+6λ+4m2
B
(
q2+5m2Klowast
2
)))
minus3CTF1m2Klowast
2
(
3m2B+m2
Klowast
2minusq2
)
34 Helicity fractions
Helicity fraction is an observable associated with polarization of the out going meson that
is almost free of hadronic uncertainties The spin-2 polarization tensor which satisfies
ǫmicroνkν = 0 with k being the momentum is symmetric and traceless It can be constructed
by the vector polarization ǫmicro as
ǫmicroν(plusmn2) = ǫmicro(plusmn)ǫν(plusmn) ǫmicroν(plusmn1) =1radic2[ǫmicro(plusmn)ǫν(0) + ǫmicro(0)ǫν(plusmn)]
ǫmicroν(0) =1radic6[ǫmicro(+)ǫν(minus) + ǫmicro(minus)ǫν(+)] +
radic
2
3ǫmicro(0)ǫν(0) (320)
ndash 12 ndash
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
In SM the zero crossing of the AFB(q2) in B rarr Klowastl+lminus is at a well determined
position which is free from the hadronic certainties at the leading order (LO) in strong
coupling αs [11ndash13] Recently the LHCb has announced the results of AFB for the decay
B rarr Klowastmicro+microminus that are close to the SM predictions They have collected over 300 events
for this decay with signal to background ratio above 3 which is the largest sample of such
decays in the world and is even cleaner than the sample used by the B factories These
results of AFB(B rarr Klowastmicro+microminus) are close to the SM predictions with slight error bars thus
they have overwritten the earlier measurements by Belle with better statistics [15] The
collaboration plans to continue to study the channel B rarr Klowastmicro+microminus in finer detail with
measurements that include more angular variables and expected to achieve high sensitivity
to any small deviation from the SM [15]
In order to incorporate the experimental predictions of different physical observables
in B rarr Klowastmicro+microminus this decay has been studied in SM and in number of different NP scenar-
ios [10 12 16ndash36] where NP effects display themselves through modification in the Wilson
coefficients as well as through the new operators Beside these models the general analysis
of B rarr Klowastmicro+microminus decay has also been performed which allow us to include all possible
NP effects like vector-axial vector (V A) scalar-pseudoscalar (SP ) and tensor-axial tensor
(TE) [37] This study has shown that the interference of V A operators among themselves
and with the SM operators is the cause of the larger magnitude of AFB(q2) as well as the
shift in the zero position of the AFB(q2) In addition to this it is also pointed out that the
SP and T operators not only influence the AFB(q2) but also give viable effects in other
physical observables
In general there are two ways to search NP which are considered to resolve anomalies
in the experimental measurements One is the direct search which can be achieved by
increasing the energies of colliders and find the predicted new particles but these particles
are quite massive and therefore hard to produced The other one is indirect search which
is comparatively easier ie to see how much different observables are affected by these new
particles The indirect searches require precise measurement of the observables for the
channel under consideration as well as need rigorous complementary studies
It is therefore indispensable to study the impact of NP on the different observables for
the decay channels other than the B rarr Klowastmicro+microminus With this motivation the B rarr Klowast2ℓ
+ℓminus
channel where Klowast2 is the excited state of Klowast with parity 2+ provide the same testing
ground to study the effects of the NP as B rarr Klowastmicro+microminus decay The exclusive B rarrKlowast
2 (1430)ℓ+ℓminus decay has been studied in the SM and some approaches beyond SM [38ndash46]
For example in refs [38 39] the form factors for B rarr Klowast2ℓ
+ℓminus are calculated using pertur-
bative QCD and LCSR approaches The analysis of different physical observable for this
decay is studied in various beyond SM scenarios like SM4 non-universal Z prime model Uni-
versal Extra dimension model and a model with the flipped sign of Ceff7 has been performed
in [40ndash42 45] The analysis of lepton polarization asymmetries of B rarr Klowast2ℓ
+ℓminus in the pres-
ence of new right-handed currents is done in [43 44] The analysis of polarized decay width
and forward-backward asymmetry by considering beyond SM operator basis is given in [46]
These studies show that like B rarr Klowastℓ+ℓminus decay this channel is also quite promising in
finding NP and will provide us some independent tests of the physics of the SM and beyond
ndash 2 ndash
JHEP02(2012)045
In this paper we will perform the study of B rarr Klowast2 (1430)micro
+microminus on the lines of ref [37]
and study the NP effects without restricting ourselves to any specific model Contrary to
B rarr Klowastmicro+microminus the decay B rarr Klowast2 (1430)micro
+microminus is not yet experimentally observed We have
taken into account the constraints from the different B decay mode such as Bs rarr micro+microminus
B rarr Xsmicro+microminus and B rarr Klowastmicro+microminus on different NP operator couplings allowed by the
most general lorentz structure of transition matrix elements In this paper we will also
incorporate bounds on the input parameters coming from the recent AFB measurements
at LHCb experiment for the decay B rarr Klowast(892)micro+microminus [15] With these new bounds we
will obtain better understanding of how these new physics operators affect branching ratio
zero-position of forward-backward asymmetry different lepton polarization asymmetries
and the helicity fractions of final state meson
The effects of these new operators couplings (VASPT) are significant to the zero
position of AFB(q2) as well as on its magnitude In addition to AFB these NP operators
also give significant effects on decay rate lepton polarization asymmetries and longitudinal
and transverse helicities of final state Klowast2 (1430) meson We hope that in the coming years
the LHCb experiment will collect around 64k events in the full range of q2 for an integrated
luminosity of 2fbminus1 [37] This would allow us to observe the B rarr Klowast2 (1430)micro
+microminus in the
SM and would also permit many of the additional tests of NP
The paper is organized as follows in section 2 the necessary hadronic inputs namely
basic Hamiltonian and form factors and constraints on the NP parameters are collected
Section 3 contains the analytic formulas for differential decay rates forward backward
asymmetry different polarizations (longitudinal normal and transverse) and the helicity
fractions of the final state Klowast2 (1430) meson Section 4 deals with the numerical analysis
and then conclusions are summarized in section 5
2 B rarr Klowast
2(1430)micro+microminus operators and matrix elements
21 Standard model
The semileptonic decay mode B rarr Klowast2 (1430)l
+lminus where l = micro for our case is governed
by the quark level transitions b rarr sl+lminus In SM the effective Hamiltonian corresponding
to this transition is given by
HSMeff = minus4GFradic
2V lowasttbVts
10sum
i=1
Ci(micro)Oi(micro) (21)
where Oi(micro)(i = 1 10) are four quark operators and Ci(micro) are the corresponding Wilson
coefficients Out of these 10 operators the O7 O9 and O10 are the relevant for B rarrKlowast
2 (1430)l+lminus decay and these can be written as
O7 =e
16π2[sσmicroν (msPL +mbPR) b]F
microν
O9 =e
16π2[sγmicroPLb]
(
lγmicrol)
O10 =e
16π2[sγmicroPLb]
(
lγmicroγ5l)
(22)
with PLR = (1plusmn γ5) 2
ndash 3 ndash
JHEP02(2012)045
In term of these operators the effective Hamiltonian for B rarr Klowast2 (1430)l
+lminus takes the
form
HSMeff = minusGFαradic
2πVtbV
lowastts
CSM9 (sγmicroPLb)(lγ
microl) + CSM10 (sγmicroPLb)(lγ
microγ5l)
minus2mbCSM7 (siσmicroν
qν
q2PRb)(lγ
microl)
(23)
where q2 is square of the sum of the momentum of final state leptons At the scale micro =
48GeV the SM Wilson coefficients takes the following values which are calculated at next-
to-next-to-leading order
Ceff7 = minus034 Ceff
9 = 4211 + Y (q2) C10 = minus4103 (24)
where Ceff7 = C7 minus C33minus 4C49minus 20C53minus 80C69 The function Y (q2) is given by
Y (z q2) = h(z q2)(3C1(micro) + C2(micro) + 3C3(micro) + C4(micro) + 3C5(micro) + C6(micro))
minus1
2h(1 sprime)(4C3(micro) + 4C4(micro) + 3C5(micro) + C6(micro))
minus1
2h(0 q2)(C3(micro) + 3C4(micro)) +
2
9(3C3(micro) + C4(micro) + 3C5(micro) + C6(micro)) (25)
with
h(z q2) = minus8
9lnz +
8
27+
4
9xminus 2
9(2 + x)|1minus x|12
ln∣
∣
∣
radic1minusx+1radic1minusxminus1
∣
∣
∣minus iπ for x equiv 4z2q2 lt 1
2 arctan 1radicxminus1
for x equiv 4z2q2 gt 1
h(0 q2) =8
27minus 8
9lnmb
microminus 4
9lnq2 +
4
9iπ (26)
and z = mcmb
22 New physics operators
The NP effects in semileptonic B meson decays can be established in two ways in one case
we can change the Wilson Coefficients but leave the operator basis same as that of the SM
and in other case we can add new operators too Here we do not restrict ourself to any
model and discuss all possible operators that corresponds to B rarr Klowast2 (1430)l
+lminus decays
In this scenario the total effective Hamiltonian for brarr sl+lminus can be written as
Heff = HSMeff +HV A
eff +HSPeff +HT
eff (27)
where HSMeff is given in eq (23) while [37]
HV Aeff =minus 4GFradic
2
α
4πV lowasttsVtb RV (sγmicroPLb) microγmicromicro+RA (sγmicroPLb) microγmicroγ5micro
+RprimeV (sγmicroPRb) microγmicromicro+Rprime
A (sγmicroPRb) microγmicroγ5micro
(28)
HSPeff =minus 4GFradic
2
α
4πV lowasttsVtb RS (sPRb) micromicro+RP (sPRb) microγ5micro
+RprimeS (sPLb) micromicro+Rprime
P (sPLb) microγ5micro
(29)
HTeff =minus 4GFradic
2
α
4πV lowasttsVtb
CT (sσmicroνb) microσmicroνmicro+ iCTE (sσmicroνb) microσαβmicroǫmicroναβ
(210)
ndash 4 ndash
JHEP02(2012)045
Here RV RA RV RprimeA RS RP R
primeS R
primeP CT and CTE are the NP effective couplings The
constraints on the numerical values of these NP coupling from different B meson decays
will be given later in this section
23 Parametrization of matrix elements and form factors
The exclusive B rarr Klowast2 (1430)l
+lminus decay involves the hadronic matrix elements of quark
operators which can be parameterized in terms of form factors These form factors are
written as
lang
Klowast2 (k ǫ) |sγmicrob|B(p)
rang
= minus 2V (q2)
mB +mKlowast
2
ǫmicroνρσεlowastναp
α
mBpρkσ (211)
lang
Klowast2 (k ǫ)
∣
∣sγmicroγ5b∣
∣B(p)rang
=2imKlowast
2A0(q
2)
q2εlowastναp
α
mBqνqmicro
+i(mB +mKlowast
2)A1(q
2)
mB
[
gmicroνεlowastναpα minus 1
q2εlowastναp
αqνqmicro]
minusiA2(q2)
εlowastναpαqν
mB(mB +mKlowast
2)
[
(pmicro + kmicro)minusm2
B minusm2Klowast
2
q2qmicro
]
(212)lang
Klowast2 (k ǫ) |sσmicroνqνb|B(p)
rang
= minus2iT1(q2)ǫmicroνρσ
εlowastναpα
mBpρkσ (213)
lang
Klowast2 (k ǫ)
∣
∣sσmicroνγ5qνb∣
∣B(p)rang
= T2(q2)[
(m2B minusm2
Klowast
2)gmicroνεlowastναp
α minus εlowastναpαqν(pmicro + kmicro)
] 1
mB
+T3(q2)εlowastναp
α
mBqν
[
qmicro minus q2
m2B minusm2
Klowast
2
(pmicro + kmicro)
]
(214)
lang
Klowast2 (k ǫ) |sb|B(p)
rang
=2V (q2)
(mB +mKlowast
2)(mb minusms)
ǫmicroνρσεlowastναp
α
mBpρkσ (215)
lang
Klowast2 (k ǫ)
∣
∣sγ5b∣
∣ B(p)rang
=2imKlowast
2A0(q
2)
q2εlowastναp
α
mB(mb +ms)qνqmicro (216)
lang
Klowast2 (k ǫ) |sσmicroνb|B(p)
rang
= minus2T1(q2)ǫmicroνρσ
εlowastναpα
mBpρkσ (217)
where p(k) is the momentum of the B(Klowast2 ) meson and εlowastνα is the polarization of the final
state Klowast2 (1430) meson In case of the tensor meson the polarization sum is given by [38]
Pmicroναβ =sum
εmicroν(p)εlowastαβ(p) =
1
2(θmicroαθνβ + θmicroβθνα)minus
1
3(θmicroνθαβ) (218)
with
θmicroν = minusgmicroν +kmicrokνm2
Klowast
2
(219)
Defining
εlowastν = εlowastναpαmB (220)
the resulting matrix elements for B rarr Klowast2 (1430) will look just like the B rarr V (eg Klowast
meson) transitions The form factors for B rarr Klowast2 (1430) transition are the non-perturbative
ndash 5 ndash
JHEP02(2012)045
F (q2) F (0) a b
V (q2) 016+002minus002 208 15
A0(q2) 025+004
minus004 157 01
A1(q2) 014+002
minus002 123 049
A2(q2) 005+002
minus002 132 149
T1(q2) 014+002
minus002 207 15
T2(q2) 014+002
minus002 122 034
T3(q2) 001+001
minus002 991 276
Table 1 B rarr Klowast
2 form factors in the light cone sum rules approach F (0) denotes the value
of form factors at q2 = 0 while a and b are the parameters in the parameterizations shown in
eq (221) [39]
quantities and are needed to be calculated using different approaches (both perturbative
and non-perturbative) like Lattice QCD QCD sum rules Light Cone sum rules etc Here
we will consider the form factors calculated in the LCSR approach [39] and their evolution
with q2 is given by
F (q2) =F (0)
1minus a(q2m2B) + b(q2m2
B)2
(221)
where the value of different parameters is given in table 1
The errors in the values of the form factors arise from number of input parameters
involved in their calculation in LCSR such as variations in the Boral parameters fluctuation
of threshold parameters errors in the b quark mass corrections from the decay constants
of involved mesons and from the Gengenbauer moments in the distribution amplitudes
It is worth mentioning here that it is possible to study this mode with the help of
QCD factorization which might discover additional sources of theoretical errors which are
overlooked in the simple form factor analysis As besides the factorizable contribution of
form factors which has been used here there are in principle non-factorizable contributions
to matrix elements as well [13] QCD factorization not only reduce the number of inde-
pendent parameters in heavy quark limit but also help us to compute the non-factorizable
corrections to B meson decays with the help of light-cone distribution amplitudes and
hard scattering kernel [53 54] The details of QCD factorization and its implications in
semileptonic and radiative B meson decays can be found in [13]
24 Numerical constraints on NP parameters
The constraints on NP parameters can be obtained from the branching ratios of B0s rarr
micro+microminus B0s rarr Xsmicro
+microminus and B0d rarr Kmicro+microminus [5 47ndash50] Due to the large hadronic uncertain-
ties the constraints obtained from the exclusive decay modes are somewhat weaker com-
pared to the inclusive ones The branching ratio of inclusive decay mode B rarr Xsmicro+microminus has
been measured by Babar [49] and Belle [50] and their measurements in low-q2 (1GeV2 le
ndash 6 ndash
JHEP02(2012)045
q2 le 6GeV2) and high-q2 (144GeV2 le q2 le 25GeV2) regions can be summarized as
B(B rarr Xsmicro+microminus)low q2 = (149plusmn 050+041
minus032)times 10minus6 (Belle)
(18plusmn 07plusmn 050)times 10minus6 (BaBar) (222)
(160plusmn 050)times 10minus6 (Average)
B(B rarr Xsmicro+microminus)high q2 = (042plusmn 012+007
minus007)times 10minus6 (Belle)
(050plusmn 025+007minus008)times 10minus6 (BaBar) (223)
(044plusmn 012)times 10minus6 (Average)
where q2 is the invariant mass squared of two muons and low-q2 region corresponds to
1GeV2 le q2 le 6GeV2 and high-q2 region corresponds to q2 ge 144GeV2
The constraints on the new V A couplings come mainly from B0d rarr Xsmicro
+microminus and B0d rarr
Kmicro+microminus [51] It has been shown in ref [51] that if RVA couplings are present only the
constraints on these couplings from above said decays came to be
10 le |RV + 36|2(47)2
+|RA minus 40|2
(48)2|RV + 28|2
(65)2+|RA minus 41|2
(66)2le 1 (224)
Similarly when we have only RprimeVA couplings the constraints on them from the same decay
will become [51]
22 le |RprimeV + 36|2 + |Rprime
A minus 40|2 le 566 |RprimeV |2 + |Rprime
A|2 le 17 (225)
These constraints are weekend when both RVA and RprimeVA couplings are present at the same
time In this case these new physics couplings are restricted to be
|RV + 28|2(65)2
+|RA minus 41|2
(66)2le 1 (226)
and
|RprimeV |2 + |Rprime
A|2 le 40 (227)
The limits on couplings corresponding to scalar-pseudoscalar (SP) operators comes
from the upper bound on B0s rarr micro+microminus which provides the limit
|RS minusRprimeS |2 + |RP minusRprime
P |2 le 044 (228)
This puts a sever constraint on the NP couplings if only RSP or RprimeSP are present However
under the condition where both types of operators are present RSP or RprimeSP these bounds
can be relaxed due to cancelation between the RSP and RprimeSP In this case B0
d rarr Xsmicro+microminus
and B0d rarr Kmicro+microminus can still bound these couplings and the stronger bound is obtained from
the measurement of later quantity which yields
|RS |2 + |RP |2 le 9 RS asymp RprimeS RS asymp Rprime
P (229)
Now the constraint on the NP tensor type couplings comes entirely from the inclusive
B0d rarr Xsmicro
+microminus decay In case when only tensor type operators are present the limits on
tensor type couplings are [51]
|CT |2 + |CTE |2 le 10 (230)
ndash 7 ndash
JHEP02(2012)045
In the present study we will examine B rarr Klowast2 (1430)micro
+microminus decays by using these NP
constraints
3 Decay rate forward-backward asymmetry and lepton polarization a-
symmetries for B rarr Klowast
2(1430)micro+microminus decay
In this section we are going to perform the calculations of some very interesting quantities
like the decay rate the forward-backward asymmetry the polarization asymmetries of
the final state lepton and the helicity fractions of the final state Klowast2 (1430) meson From
eq (27) it is straightforward to obtain the decay amplitude for B rarr Klowast2 (1430)micro
+microminus as
M(B rarr Klowast2 (1430)micro
+microminus) = minus GFα
2radic2π
VtbVlowastts
[
TmicroV lγmicrol + Tmicro
A lγmicroγ5l
+TS ll + TP lγ5l + Tmicroν
T lσmicroν l + iTmicroνE ǫmicroναβ lσαβl
]
(31)
with
TmicroV = minusF1ǫ
microναβεlowastνpKlowastαqβ + iF2εlowastmicro + iF3ε
lowast middot q(pB + pKlowast)micro + iF4εlowast middot qqmicro
TmicroA = minusF5ǫ
microναβεlowastνpKlowastαqβ + iF6εlowastmicro + iF7ε
lowast middot q(pB + pKlowast)micro + iF8εlowast middot qqmicro
TS = iF9εlowast middot q
TP = iF10εlowast middot pB
TmicroνT = CT
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
TmicroνE = CTE
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
(32)
The auxiliary functions F1 middot middot middot F13 appearing in eq (32) are defined as follows
F1 =
[
2V (q2)
mB +mKlowast
(Ceff9 +RV +Rprime
V ) +4mb
q2Ceff7 T1(q
2)
]
F2 = minus[
(mB +mKlowast)A1(q2)(Ceff
9 +RV minusRprimeV ) +
2mb
q2Ceff7 T1(q
2)(m2B minusmKlowast)
]
F3 =
[
A(q2)
mB +mKlowast
(Ceff9 +RV minusRprime
V ) +2mb
q2Ceff7
(
T1(q2) +
q2T3(q2)
m2B minusmKlowast
)]
F4 =
[
2mKlowast
q2(Ceff
9 +RV minusRprimeV )(A3(q
2)minusA0(q2))minus 2mb
q2Ceff7 T3(q
2)
]
F5 =
[
2V (q2)
mB +mKlowast
(Ceff10 +RA +Rprime
A)
]
F6 = minus[
(mB +mKlowast)A1(q2)(Ceff
10 +RA minusRprimeA)
]
F7 =
[
A(q2)
mB +mKlowast
(Ceff10 +RA minusRprime
A)
]
F8 =
[
2mKlowast
q2(Ceff
10 +RA minusRprimeA)(A3(q
2)minusA0(q2))
]
F9 =
[
minus2(RS minusRprimeS)
mKlowast
mbA0(q
2)
]
ndash 8 ndash
JHEP02(2012)045
F10 =
[
2(RP minusRprimeP )
mKlowast
mbA0(q
2)
]
F11 = minus2T1(q2)
F12 =
[
2(m2B minusm2
Klowast)
q2(T1(q
2)minus T2(q2))
]
F13 =
[
4
q2
(
T1(q2)minus T2(q
2)minus q2T3(q2)
m2B minusm2
Klowast
)]
(33)
31 Differential decay rate
The differential decay width of B rarr Klowast2 (1430)micro
+microminus in dilepton center of mass frame can
be written as
dΓ(B rarr Klowast2 (1430)micro
+microminus)
dq2=
1
(2π)31
32m3B
int u(q2)
minusu(q2)|MBrarrKlowast
2(1430)micro+microminus |2du (34)
where u = (p + pmicrominus)2 minus (p + pmicro+)2 = u(q2) cos θ and q2 = (pmicro+ + pmicrominus)2 p k pmicro+ and
pmicrominus are the four-momenta vectors of B Klowast2 (1430) micro
+ and microminus respectively and u(q2) are
given by
u(q2) =radic
m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2
radic
1minus 4m2l
q2(35)
Collecting everything together one can write the general expression of the differential decay
rate for B rarr Klowast2 (1430)micro
+microminus as
dΓ
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
18m2lm
4T q
2
3F21m
2Klowast
2q2λ+ 2F2
2m4B(λ+ 10m2
T q2) (36)
+2F23λ
2] (
2m2l + q2
)
minus[
3F25m
2Klowast
2minus 3F2
9m2B
]
K2q2λ+ 12F2
8m2l q
4λ
+2F26m
4B
[
2(
λminus 20m2T q
2)
m2l + q2
(
λ+ 10m2T q
2)]
+ 3F210m
2Bq
4λ
+2F27λ
[
2(
λminus 3q4 + 6m2T q
2)
m2Klowast
2+ q2λ
]
minus 4F2F3m4B
(
2m2l + q2
)
K1λ2
minus4F6F7m2Bλ
[
2(
K1 + 3q2)
m2l +K1q
2]
minus 24F6F8m2lm
2Bq
2λminus 12F10F6mlm3Bq
2λ
+24F7F8m2lK0q
2λ+ 12F10F7mlmBK0q2λ+ 8F11F12q
2(λ+ 10m2Tm
2B minus 10m4
T )K3
minus4F11F13(K1 + 4m2T )λq
2K3 minus 72F1F11mlm2Klowast
2q2λCT
+48F11F2mlm2Bq
2(λ+ 10m2Tm
2B minus 10m4
T )CTE minus 4F12F13K1λq2K3
+48F12F2mlm2Bq
2(
λ+ 10m2T q
2)
CTE minus 48F12F3mlq2K1CTEλ
minus24F13F2mlm2BK1λq
2CTE + 24F13F3mlq2CTEλ
2
where ml is the mass of final state muon and
λ = λ(
m2Bm
2Klowast
2 q2
)
equiv m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2 (37)
K0 = (m2B minusm2
Klowast
2) K1 =
(
m2B minusm2
Klowast
2minus q2
)
K2 = q2 minus 4m2l
K3 = q2C2T minus 4m2
l
(
C2T minus 36C2
TE
)
(38)
and the auxiliary functions are the same as defined in eq (33)
ndash 9 ndash
JHEP02(2012)045
32 Forward-backward asymmetry
Now we are in a position to explore the forward-backward asymmetry of final state leptons
in the B rarr Klowast2 (1430)micro
+microminus which is an essential observable sensitive to the new physics
effects To calculate the forward-backward asymmetry we consider the following double
differential decay rate formula for the process B rarr Klowast2 (1430)micro
+microminus
d2Γ(q2 cos θ)
dq2d cos θ=
1
(2π)31
64m3B
u(q2)|MBrarrKlowast
2(1430)micro+microminus |2 (39)
where θ is the angle between the momentum of B baryon and lminus in the dilepton rest frame
The differential and normalized FBAs for the semi-leptonic decay B rarr Klowast2 (1430)l
+lminus are
defined as
dAFB(q2)
dq2=
int 1
0d cos θ
d2Γ(q2 cos θ)
dq2d cos θminusint 0
minus1d cos θ
d2Γ(q2 cos θ)
dq2d cos θ(310)
and
AFB(q2) =
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θminusint 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θ+int 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
(311)
Following the same procedure as we did for the differential decay rate one can easily get
the expression for the forward-backward asymmetry as follows
dAFB(q2)
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
6mBm4T
[
AV AFB +ASP
FB +ATSPFB +AT
FB
]
(312a)
AV AFB = minus3(F2F5 + F1F6)q
2m2Bm
2K2
(312b)
ASPFB = 2F9mlmB
(
F3λ+ F2m2B
[
q2 minusm2B +m2
K2
])
(312c)
ATSPFB = minusq2 (F10CT + 2F9CTE)mB
(
2F12
(
m2B minusm2
K2minus q2
)
(312d)
minusF13λ+ 2F11
(
m2B + 3m2
K2minus q2
))
ATFB = minus2ml
(
12F12F5q2CTEm
2K2
+ 12F11F5CTEm2K2
(
m2B minusm2
K2
)
(312e)
+F13λCT
(
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F12CT
(
m2B minusm2
K2minus q2
) (
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F11CT
(
F6m2B
(
m2B + 9m2
K2minus q2
)
minus(
m2B + 3m2
K2minus q2
) (
F8q2 + F7
(
m2B minusm2
K2
)))
and the expression of the differential decay rate is given in eq (36)
33 Lepton polarization asymmetries
In the rest frame of the lepton microminus the unit vectors along longitudinal normal and transver-
sal component of the microminus can be defined as [55]
sminusmicroL = (0 ~eL) =
(
0~pminus|~pminus|
)
sminusmicroN = (0 ~eN ) =
0~k times ~pminus∣
∣
∣
~k times ~pminus∣
∣
∣
(313)
sminusmicroT = (0 ~eT ) = (0 ~eN times ~eL)
ndash 10 ndash
JHEP02(2012)045
where ~pminus and ~k are the three-momenta of the microminus and Klowast2 (1430) meson respectively in the
center mass (CM) frame of micro+microminus system Lorentz transformation is used to boost the
longitudinal component of the lepton polarization to the CM frame of the lepton pair as
(
sminusmicroL
)
CM=
( |~pminus|ml
El~pminusml |~pminus|
)
(314)
where El and ml are the energy and mass of the final state muon The normal and
transverse components remain unchanged under the Lorentz boost The longitudinal (PL)
normal (PN ) and transverse (PT ) polarizations of lepton can be defined as
P(∓)i (q2) =
dΓdq2
(~ξ∓ = ~e∓)minus dΓdq2
(~ξ∓ = minus~e∓)dΓdq2
(~ξ∓ = ~e∓) + dΓdq2
(~ξ∓ = minus~e∓)(315)
where i = L N T and ~ξ∓ is the spin direction along the leptons micro∓ The differential
decay rate for polarized lepton l∓ in B rarr Klowast2 (1430)micro
+microminus decay along any spin direction~ξ∓ is related to the unpolarized decay rate (36) with the following relation
dΓ(~ξ∓)
dq2=
1
2
(
dΓ
dq2
)
[1 + (P∓L ~e∓L + P∓
N~e∓N + P∓T ~e∓T ) middot ~ξ∓] (316)
We can achieve the expressions of longitudinal normal and transverse polarizations for
B rarr Klowast2 (1430)micro
+microminus decays as collected below The longitudinal lepton polarization can
be written as
PL prop1
36m2Bm
4T
4u(q2)radicλ[
P V AL + PSP
L + P TL
]
(317a)
P V AL = ml
(
2λF2 (F6 minusF7)m4B +
(
3λF1F5q2 + 2F2m
2B
(
10q2F6m2B + λF7
))
m2Klowast
2
+2λF3
(
F6
(
q2 minusm2B +m2
Klowast
2
)
m2B + λF7
))
(317b)
PSPL = 3mlλF9mB
(
minus2mlF8q2 minusF10mBq
2 + 2ml
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
(317c)
P TL = m2
lF11
(
24 (CTEF1 minus CTF5)m2Klowast
2λ+ 4CTλF3
(
m2B + 3m2
Klowast
2minus q2
)
+4m2B (4CTEF6 minus CTF2)
(
10(
m2B minusm2
Klowast
2
)
m2Klowast
2+ λ
))
+m2lF12
(
4m2B (4CTEF6 minus CTF2)
(
10q2m2Klowast
2+ λ
)
minus 4CTF3
(
q2 minusm2B +m2
Klowast
2
))
+m2lF13
(
2CTλminus 4CTF2m2B
(
m2B minusm2
Klowast
2minus q2
)
minus 2CTλ2F3
)
(317d)
ndash 11 ndash
JHEP02(2012)045
Similarly the normal lepton polarization is
PN prop minusπu(q2)t
(12m2Bm
4T
(λ
t)32
[
P V AN + PSP
N + P TN
]
(318a)
P V AN = 2ml
(
F2
(
F8q4 minus
(
(F6 minusF7 + F8)m2B + (minus3F1 + F7 minusF8)m
2Klowast
2
)
q2 (318b)
+(
m2B minusm2
Klowast
2
)
m2B
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
+ λF3
(
F8q2 minusF6m
2B + F7
(
m2B minusm2
Klowast
2
)))
PSPN = mBλ
(
F3F10q2 +
(
q2 minus 4m2l
)
F7F9
)
(318c)
minus(
F2F10q2 +
(
q2 minus 4m2l
)
F6F9
)
m3B
(
m2B minusm2
Klowast
2minus q2
)
P TN = F13
(
8m2l λCTE
(
F8q2 minusF6m
2B minusF7
(
m2Klowast
2minusm2
B
))
+ 4mlmBλCTEF10q2)
+F12
(
16m2lCTE
(
F6m2BminusF7
(
m2Bminusm2
Klowast
2
)
minusF8q2minusmB
2mlF10q
2
)
(
m2Bminusm2
Klowast
2minusq2
)
+ 6(
4m2l + q2
)
CTEF1q2m2
Klowast
2+ 3
(
q2 minus 4m2)
CTF5q2m2
Klowast
2
)
+F11
(
minus16m2lCTE
(
F8q2 + F7
(
m2B minusm2
Klowast
2
)
+mB
2mlF10q
2
)
(
m2B + 3m2
Klowast
2minus q2
)
+6m2Klowast
2
(
4m2l + q2
)
(
CTEF1
(
m2B minusm2
Klowast
2
)
minus CTF2m2B
)
+3(
4m2l minus q2
)
CTF5m2Klowast
2
(
m2Klowast
2minusm2
B
)
+4CTEF6m2B
(
4m2l
(
m2B + 6m2
Klowast
2minus q2
)
minus 3q2m2Klowast
2
)
)
(318d)
and the transverse one is given by
PT propiπλq2u(q2)
12mBm2Klowast
2
λCTEF13
(
4F2m2B minus 3F5m
2Klowast
2+ F3
(
q2 minus 5m2B +m2
Klowast
2
))
(319)
minus2F12
(
2CTE
((
8F3m2B minus (2F3 + 3F5)m
2Klowast
2
)
q2 + 4F2m2B
(
2m2B +m2
Klowast
2minus 2q2
)
minus(
m2Bminusm2
Klowast
2
)(
8F3m2B + (4F3 + 3F5)m
2Klowast
2
))
minus3CTF1m2Klowast
2
(
q2minus3m2B + 3m2
Klowast
2
))
+2F11
(
2CTE
(
3F5m2Klowast
2
(
3m2B +m2
Klowast
2minus q2
)
minus 4F2
(
2m2B + 3m2
Klowast
2minus 2q2
)
m2B
+2F3
(
7m2Klowast
2q2minus4q4+6λ+4m2
B
(
q2+5m2Klowast
2
)))
minus3CTF1m2Klowast
2
(
3m2B+m2
Klowast
2minusq2
)
34 Helicity fractions
Helicity fraction is an observable associated with polarization of the out going meson that
is almost free of hadronic uncertainties The spin-2 polarization tensor which satisfies
ǫmicroνkν = 0 with k being the momentum is symmetric and traceless It can be constructed
by the vector polarization ǫmicro as
ǫmicroν(plusmn2) = ǫmicro(plusmn)ǫν(plusmn) ǫmicroν(plusmn1) =1radic2[ǫmicro(plusmn)ǫν(0) + ǫmicro(0)ǫν(plusmn)]
ǫmicroν(0) =1radic6[ǫmicro(+)ǫν(minus) + ǫmicro(minus)ǫν(+)] +
radic
2
3ǫmicro(0)ǫν(0) (320)
ndash 12 ndash
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
In this paper we will perform the study of B rarr Klowast2 (1430)micro
+microminus on the lines of ref [37]
and study the NP effects without restricting ourselves to any specific model Contrary to
B rarr Klowastmicro+microminus the decay B rarr Klowast2 (1430)micro
+microminus is not yet experimentally observed We have
taken into account the constraints from the different B decay mode such as Bs rarr micro+microminus
B rarr Xsmicro+microminus and B rarr Klowastmicro+microminus on different NP operator couplings allowed by the
most general lorentz structure of transition matrix elements In this paper we will also
incorporate bounds on the input parameters coming from the recent AFB measurements
at LHCb experiment for the decay B rarr Klowast(892)micro+microminus [15] With these new bounds we
will obtain better understanding of how these new physics operators affect branching ratio
zero-position of forward-backward asymmetry different lepton polarization asymmetries
and the helicity fractions of final state meson
The effects of these new operators couplings (VASPT) are significant to the zero
position of AFB(q2) as well as on its magnitude In addition to AFB these NP operators
also give significant effects on decay rate lepton polarization asymmetries and longitudinal
and transverse helicities of final state Klowast2 (1430) meson We hope that in the coming years
the LHCb experiment will collect around 64k events in the full range of q2 for an integrated
luminosity of 2fbminus1 [37] This would allow us to observe the B rarr Klowast2 (1430)micro
+microminus in the
SM and would also permit many of the additional tests of NP
The paper is organized as follows in section 2 the necessary hadronic inputs namely
basic Hamiltonian and form factors and constraints on the NP parameters are collected
Section 3 contains the analytic formulas for differential decay rates forward backward
asymmetry different polarizations (longitudinal normal and transverse) and the helicity
fractions of the final state Klowast2 (1430) meson Section 4 deals with the numerical analysis
and then conclusions are summarized in section 5
2 B rarr Klowast
2(1430)micro+microminus operators and matrix elements
21 Standard model
The semileptonic decay mode B rarr Klowast2 (1430)l
+lminus where l = micro for our case is governed
by the quark level transitions b rarr sl+lminus In SM the effective Hamiltonian corresponding
to this transition is given by
HSMeff = minus4GFradic
2V lowasttbVts
10sum
i=1
Ci(micro)Oi(micro) (21)
where Oi(micro)(i = 1 10) are four quark operators and Ci(micro) are the corresponding Wilson
coefficients Out of these 10 operators the O7 O9 and O10 are the relevant for B rarrKlowast
2 (1430)l+lminus decay and these can be written as
O7 =e
16π2[sσmicroν (msPL +mbPR) b]F
microν
O9 =e
16π2[sγmicroPLb]
(
lγmicrol)
O10 =e
16π2[sγmicroPLb]
(
lγmicroγ5l)
(22)
with PLR = (1plusmn γ5) 2
ndash 3 ndash
JHEP02(2012)045
In term of these operators the effective Hamiltonian for B rarr Klowast2 (1430)l
+lminus takes the
form
HSMeff = minusGFαradic
2πVtbV
lowastts
CSM9 (sγmicroPLb)(lγ
microl) + CSM10 (sγmicroPLb)(lγ
microγ5l)
minus2mbCSM7 (siσmicroν
qν
q2PRb)(lγ
microl)
(23)
where q2 is square of the sum of the momentum of final state leptons At the scale micro =
48GeV the SM Wilson coefficients takes the following values which are calculated at next-
to-next-to-leading order
Ceff7 = minus034 Ceff
9 = 4211 + Y (q2) C10 = minus4103 (24)
where Ceff7 = C7 minus C33minus 4C49minus 20C53minus 80C69 The function Y (q2) is given by
Y (z q2) = h(z q2)(3C1(micro) + C2(micro) + 3C3(micro) + C4(micro) + 3C5(micro) + C6(micro))
minus1
2h(1 sprime)(4C3(micro) + 4C4(micro) + 3C5(micro) + C6(micro))
minus1
2h(0 q2)(C3(micro) + 3C4(micro)) +
2
9(3C3(micro) + C4(micro) + 3C5(micro) + C6(micro)) (25)
with
h(z q2) = minus8
9lnz +
8
27+
4
9xminus 2
9(2 + x)|1minus x|12
ln∣
∣
∣
radic1minusx+1radic1minusxminus1
∣
∣
∣minus iπ for x equiv 4z2q2 lt 1
2 arctan 1radicxminus1
for x equiv 4z2q2 gt 1
h(0 q2) =8
27minus 8
9lnmb
microminus 4
9lnq2 +
4
9iπ (26)
and z = mcmb
22 New physics operators
The NP effects in semileptonic B meson decays can be established in two ways in one case
we can change the Wilson Coefficients but leave the operator basis same as that of the SM
and in other case we can add new operators too Here we do not restrict ourself to any
model and discuss all possible operators that corresponds to B rarr Klowast2 (1430)l
+lminus decays
In this scenario the total effective Hamiltonian for brarr sl+lminus can be written as
Heff = HSMeff +HV A
eff +HSPeff +HT
eff (27)
where HSMeff is given in eq (23) while [37]
HV Aeff =minus 4GFradic
2
α
4πV lowasttsVtb RV (sγmicroPLb) microγmicromicro+RA (sγmicroPLb) microγmicroγ5micro
+RprimeV (sγmicroPRb) microγmicromicro+Rprime
A (sγmicroPRb) microγmicroγ5micro
(28)
HSPeff =minus 4GFradic
2
α
4πV lowasttsVtb RS (sPRb) micromicro+RP (sPRb) microγ5micro
+RprimeS (sPLb) micromicro+Rprime
P (sPLb) microγ5micro
(29)
HTeff =minus 4GFradic
2
α
4πV lowasttsVtb
CT (sσmicroνb) microσmicroνmicro+ iCTE (sσmicroνb) microσαβmicroǫmicroναβ
(210)
ndash 4 ndash
JHEP02(2012)045
Here RV RA RV RprimeA RS RP R
primeS R
primeP CT and CTE are the NP effective couplings The
constraints on the numerical values of these NP coupling from different B meson decays
will be given later in this section
23 Parametrization of matrix elements and form factors
The exclusive B rarr Klowast2 (1430)l
+lminus decay involves the hadronic matrix elements of quark
operators which can be parameterized in terms of form factors These form factors are
written as
lang
Klowast2 (k ǫ) |sγmicrob|B(p)
rang
= minus 2V (q2)
mB +mKlowast
2
ǫmicroνρσεlowastναp
α
mBpρkσ (211)
lang
Klowast2 (k ǫ)
∣
∣sγmicroγ5b∣
∣B(p)rang
=2imKlowast
2A0(q
2)
q2εlowastναp
α
mBqνqmicro
+i(mB +mKlowast
2)A1(q
2)
mB
[
gmicroνεlowastναpα minus 1
q2εlowastναp
αqνqmicro]
minusiA2(q2)
εlowastναpαqν
mB(mB +mKlowast
2)
[
(pmicro + kmicro)minusm2
B minusm2Klowast
2
q2qmicro
]
(212)lang
Klowast2 (k ǫ) |sσmicroνqνb|B(p)
rang
= minus2iT1(q2)ǫmicroνρσ
εlowastναpα
mBpρkσ (213)
lang
Klowast2 (k ǫ)
∣
∣sσmicroνγ5qνb∣
∣B(p)rang
= T2(q2)[
(m2B minusm2
Klowast
2)gmicroνεlowastναp
α minus εlowastναpαqν(pmicro + kmicro)
] 1
mB
+T3(q2)εlowastναp
α
mBqν
[
qmicro minus q2
m2B minusm2
Klowast
2
(pmicro + kmicro)
]
(214)
lang
Klowast2 (k ǫ) |sb|B(p)
rang
=2V (q2)
(mB +mKlowast
2)(mb minusms)
ǫmicroνρσεlowastναp
α
mBpρkσ (215)
lang
Klowast2 (k ǫ)
∣
∣sγ5b∣
∣ B(p)rang
=2imKlowast
2A0(q
2)
q2εlowastναp
α
mB(mb +ms)qνqmicro (216)
lang
Klowast2 (k ǫ) |sσmicroνb|B(p)
rang
= minus2T1(q2)ǫmicroνρσ
εlowastναpα
mBpρkσ (217)
where p(k) is the momentum of the B(Klowast2 ) meson and εlowastνα is the polarization of the final
state Klowast2 (1430) meson In case of the tensor meson the polarization sum is given by [38]
Pmicroναβ =sum
εmicroν(p)εlowastαβ(p) =
1
2(θmicroαθνβ + θmicroβθνα)minus
1
3(θmicroνθαβ) (218)
with
θmicroν = minusgmicroν +kmicrokνm2
Klowast
2
(219)
Defining
εlowastν = εlowastναpαmB (220)
the resulting matrix elements for B rarr Klowast2 (1430) will look just like the B rarr V (eg Klowast
meson) transitions The form factors for B rarr Klowast2 (1430) transition are the non-perturbative
ndash 5 ndash
JHEP02(2012)045
F (q2) F (0) a b
V (q2) 016+002minus002 208 15
A0(q2) 025+004
minus004 157 01
A1(q2) 014+002
minus002 123 049
A2(q2) 005+002
minus002 132 149
T1(q2) 014+002
minus002 207 15
T2(q2) 014+002
minus002 122 034
T3(q2) 001+001
minus002 991 276
Table 1 B rarr Klowast
2 form factors in the light cone sum rules approach F (0) denotes the value
of form factors at q2 = 0 while a and b are the parameters in the parameterizations shown in
eq (221) [39]
quantities and are needed to be calculated using different approaches (both perturbative
and non-perturbative) like Lattice QCD QCD sum rules Light Cone sum rules etc Here
we will consider the form factors calculated in the LCSR approach [39] and their evolution
with q2 is given by
F (q2) =F (0)
1minus a(q2m2B) + b(q2m2
B)2
(221)
where the value of different parameters is given in table 1
The errors in the values of the form factors arise from number of input parameters
involved in their calculation in LCSR such as variations in the Boral parameters fluctuation
of threshold parameters errors in the b quark mass corrections from the decay constants
of involved mesons and from the Gengenbauer moments in the distribution amplitudes
It is worth mentioning here that it is possible to study this mode with the help of
QCD factorization which might discover additional sources of theoretical errors which are
overlooked in the simple form factor analysis As besides the factorizable contribution of
form factors which has been used here there are in principle non-factorizable contributions
to matrix elements as well [13] QCD factorization not only reduce the number of inde-
pendent parameters in heavy quark limit but also help us to compute the non-factorizable
corrections to B meson decays with the help of light-cone distribution amplitudes and
hard scattering kernel [53 54] The details of QCD factorization and its implications in
semileptonic and radiative B meson decays can be found in [13]
24 Numerical constraints on NP parameters
The constraints on NP parameters can be obtained from the branching ratios of B0s rarr
micro+microminus B0s rarr Xsmicro
+microminus and B0d rarr Kmicro+microminus [5 47ndash50] Due to the large hadronic uncertain-
ties the constraints obtained from the exclusive decay modes are somewhat weaker com-
pared to the inclusive ones The branching ratio of inclusive decay mode B rarr Xsmicro+microminus has
been measured by Babar [49] and Belle [50] and their measurements in low-q2 (1GeV2 le
ndash 6 ndash
JHEP02(2012)045
q2 le 6GeV2) and high-q2 (144GeV2 le q2 le 25GeV2) regions can be summarized as
B(B rarr Xsmicro+microminus)low q2 = (149plusmn 050+041
minus032)times 10minus6 (Belle)
(18plusmn 07plusmn 050)times 10minus6 (BaBar) (222)
(160plusmn 050)times 10minus6 (Average)
B(B rarr Xsmicro+microminus)high q2 = (042plusmn 012+007
minus007)times 10minus6 (Belle)
(050plusmn 025+007minus008)times 10minus6 (BaBar) (223)
(044plusmn 012)times 10minus6 (Average)
where q2 is the invariant mass squared of two muons and low-q2 region corresponds to
1GeV2 le q2 le 6GeV2 and high-q2 region corresponds to q2 ge 144GeV2
The constraints on the new V A couplings come mainly from B0d rarr Xsmicro
+microminus and B0d rarr
Kmicro+microminus [51] It has been shown in ref [51] that if RVA couplings are present only the
constraints on these couplings from above said decays came to be
10 le |RV + 36|2(47)2
+|RA minus 40|2
(48)2|RV + 28|2
(65)2+|RA minus 41|2
(66)2le 1 (224)
Similarly when we have only RprimeVA couplings the constraints on them from the same decay
will become [51]
22 le |RprimeV + 36|2 + |Rprime
A minus 40|2 le 566 |RprimeV |2 + |Rprime
A|2 le 17 (225)
These constraints are weekend when both RVA and RprimeVA couplings are present at the same
time In this case these new physics couplings are restricted to be
|RV + 28|2(65)2
+|RA minus 41|2
(66)2le 1 (226)
and
|RprimeV |2 + |Rprime
A|2 le 40 (227)
The limits on couplings corresponding to scalar-pseudoscalar (SP) operators comes
from the upper bound on B0s rarr micro+microminus which provides the limit
|RS minusRprimeS |2 + |RP minusRprime
P |2 le 044 (228)
This puts a sever constraint on the NP couplings if only RSP or RprimeSP are present However
under the condition where both types of operators are present RSP or RprimeSP these bounds
can be relaxed due to cancelation between the RSP and RprimeSP In this case B0
d rarr Xsmicro+microminus
and B0d rarr Kmicro+microminus can still bound these couplings and the stronger bound is obtained from
the measurement of later quantity which yields
|RS |2 + |RP |2 le 9 RS asymp RprimeS RS asymp Rprime
P (229)
Now the constraint on the NP tensor type couplings comes entirely from the inclusive
B0d rarr Xsmicro
+microminus decay In case when only tensor type operators are present the limits on
tensor type couplings are [51]
|CT |2 + |CTE |2 le 10 (230)
ndash 7 ndash
JHEP02(2012)045
In the present study we will examine B rarr Klowast2 (1430)micro
+microminus decays by using these NP
constraints
3 Decay rate forward-backward asymmetry and lepton polarization a-
symmetries for B rarr Klowast
2(1430)micro+microminus decay
In this section we are going to perform the calculations of some very interesting quantities
like the decay rate the forward-backward asymmetry the polarization asymmetries of
the final state lepton and the helicity fractions of the final state Klowast2 (1430) meson From
eq (27) it is straightforward to obtain the decay amplitude for B rarr Klowast2 (1430)micro
+microminus as
M(B rarr Klowast2 (1430)micro
+microminus) = minus GFα
2radic2π
VtbVlowastts
[
TmicroV lγmicrol + Tmicro
A lγmicroγ5l
+TS ll + TP lγ5l + Tmicroν
T lσmicroν l + iTmicroνE ǫmicroναβ lσαβl
]
(31)
with
TmicroV = minusF1ǫ
microναβεlowastνpKlowastαqβ + iF2εlowastmicro + iF3ε
lowast middot q(pB + pKlowast)micro + iF4εlowast middot qqmicro
TmicroA = minusF5ǫ
microναβεlowastνpKlowastαqβ + iF6εlowastmicro + iF7ε
lowast middot q(pB + pKlowast)micro + iF8εlowast middot qqmicro
TS = iF9εlowast middot q
TP = iF10εlowast middot pB
TmicroνT = CT
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
TmicroνE = CTE
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
(32)
The auxiliary functions F1 middot middot middot F13 appearing in eq (32) are defined as follows
F1 =
[
2V (q2)
mB +mKlowast
(Ceff9 +RV +Rprime
V ) +4mb
q2Ceff7 T1(q
2)
]
F2 = minus[
(mB +mKlowast)A1(q2)(Ceff
9 +RV minusRprimeV ) +
2mb
q2Ceff7 T1(q
2)(m2B minusmKlowast)
]
F3 =
[
A(q2)
mB +mKlowast
(Ceff9 +RV minusRprime
V ) +2mb
q2Ceff7
(
T1(q2) +
q2T3(q2)
m2B minusmKlowast
)]
F4 =
[
2mKlowast
q2(Ceff
9 +RV minusRprimeV )(A3(q
2)minusA0(q2))minus 2mb
q2Ceff7 T3(q
2)
]
F5 =
[
2V (q2)
mB +mKlowast
(Ceff10 +RA +Rprime
A)
]
F6 = minus[
(mB +mKlowast)A1(q2)(Ceff
10 +RA minusRprimeA)
]
F7 =
[
A(q2)
mB +mKlowast
(Ceff10 +RA minusRprime
A)
]
F8 =
[
2mKlowast
q2(Ceff
10 +RA minusRprimeA)(A3(q
2)minusA0(q2))
]
F9 =
[
minus2(RS minusRprimeS)
mKlowast
mbA0(q
2)
]
ndash 8 ndash
JHEP02(2012)045
F10 =
[
2(RP minusRprimeP )
mKlowast
mbA0(q
2)
]
F11 = minus2T1(q2)
F12 =
[
2(m2B minusm2
Klowast)
q2(T1(q
2)minus T2(q2))
]
F13 =
[
4
q2
(
T1(q2)minus T2(q
2)minus q2T3(q2)
m2B minusm2
Klowast
)]
(33)
31 Differential decay rate
The differential decay width of B rarr Klowast2 (1430)micro
+microminus in dilepton center of mass frame can
be written as
dΓ(B rarr Klowast2 (1430)micro
+microminus)
dq2=
1
(2π)31
32m3B
int u(q2)
minusu(q2)|MBrarrKlowast
2(1430)micro+microminus |2du (34)
where u = (p + pmicrominus)2 minus (p + pmicro+)2 = u(q2) cos θ and q2 = (pmicro+ + pmicrominus)2 p k pmicro+ and
pmicrominus are the four-momenta vectors of B Klowast2 (1430) micro
+ and microminus respectively and u(q2) are
given by
u(q2) =radic
m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2
radic
1minus 4m2l
q2(35)
Collecting everything together one can write the general expression of the differential decay
rate for B rarr Klowast2 (1430)micro
+microminus as
dΓ
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
18m2lm
4T q
2
3F21m
2Klowast
2q2λ+ 2F2
2m4B(λ+ 10m2
T q2) (36)
+2F23λ
2] (
2m2l + q2
)
minus[
3F25m
2Klowast
2minus 3F2
9m2B
]
K2q2λ+ 12F2
8m2l q
4λ
+2F26m
4B
[
2(
λminus 20m2T q
2)
m2l + q2
(
λ+ 10m2T q
2)]
+ 3F210m
2Bq
4λ
+2F27λ
[
2(
λminus 3q4 + 6m2T q
2)
m2Klowast
2+ q2λ
]
minus 4F2F3m4B
(
2m2l + q2
)
K1λ2
minus4F6F7m2Bλ
[
2(
K1 + 3q2)
m2l +K1q
2]
minus 24F6F8m2lm
2Bq
2λminus 12F10F6mlm3Bq
2λ
+24F7F8m2lK0q
2λ+ 12F10F7mlmBK0q2λ+ 8F11F12q
2(λ+ 10m2Tm
2B minus 10m4
T )K3
minus4F11F13(K1 + 4m2T )λq
2K3 minus 72F1F11mlm2Klowast
2q2λCT
+48F11F2mlm2Bq
2(λ+ 10m2Tm
2B minus 10m4
T )CTE minus 4F12F13K1λq2K3
+48F12F2mlm2Bq
2(
λ+ 10m2T q
2)
CTE minus 48F12F3mlq2K1CTEλ
minus24F13F2mlm2BK1λq
2CTE + 24F13F3mlq2CTEλ
2
where ml is the mass of final state muon and
λ = λ(
m2Bm
2Klowast
2 q2
)
equiv m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2 (37)
K0 = (m2B minusm2
Klowast
2) K1 =
(
m2B minusm2
Klowast
2minus q2
)
K2 = q2 minus 4m2l
K3 = q2C2T minus 4m2
l
(
C2T minus 36C2
TE
)
(38)
and the auxiliary functions are the same as defined in eq (33)
ndash 9 ndash
JHEP02(2012)045
32 Forward-backward asymmetry
Now we are in a position to explore the forward-backward asymmetry of final state leptons
in the B rarr Klowast2 (1430)micro
+microminus which is an essential observable sensitive to the new physics
effects To calculate the forward-backward asymmetry we consider the following double
differential decay rate formula for the process B rarr Klowast2 (1430)micro
+microminus
d2Γ(q2 cos θ)
dq2d cos θ=
1
(2π)31
64m3B
u(q2)|MBrarrKlowast
2(1430)micro+microminus |2 (39)
where θ is the angle between the momentum of B baryon and lminus in the dilepton rest frame
The differential and normalized FBAs for the semi-leptonic decay B rarr Klowast2 (1430)l
+lminus are
defined as
dAFB(q2)
dq2=
int 1
0d cos θ
d2Γ(q2 cos θ)
dq2d cos θminusint 0
minus1d cos θ
d2Γ(q2 cos θ)
dq2d cos θ(310)
and
AFB(q2) =
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θminusint 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θ+int 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
(311)
Following the same procedure as we did for the differential decay rate one can easily get
the expression for the forward-backward asymmetry as follows
dAFB(q2)
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
6mBm4T
[
AV AFB +ASP
FB +ATSPFB +AT
FB
]
(312a)
AV AFB = minus3(F2F5 + F1F6)q
2m2Bm
2K2
(312b)
ASPFB = 2F9mlmB
(
F3λ+ F2m2B
[
q2 minusm2B +m2
K2
])
(312c)
ATSPFB = minusq2 (F10CT + 2F9CTE)mB
(
2F12
(
m2B minusm2
K2minus q2
)
(312d)
minusF13λ+ 2F11
(
m2B + 3m2
K2minus q2
))
ATFB = minus2ml
(
12F12F5q2CTEm
2K2
+ 12F11F5CTEm2K2
(
m2B minusm2
K2
)
(312e)
+F13λCT
(
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F12CT
(
m2B minusm2
K2minus q2
) (
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F11CT
(
F6m2B
(
m2B + 9m2
K2minus q2
)
minus(
m2B + 3m2
K2minus q2
) (
F8q2 + F7
(
m2B minusm2
K2
)))
and the expression of the differential decay rate is given in eq (36)
33 Lepton polarization asymmetries
In the rest frame of the lepton microminus the unit vectors along longitudinal normal and transver-
sal component of the microminus can be defined as [55]
sminusmicroL = (0 ~eL) =
(
0~pminus|~pminus|
)
sminusmicroN = (0 ~eN ) =
0~k times ~pminus∣
∣
∣
~k times ~pminus∣
∣
∣
(313)
sminusmicroT = (0 ~eT ) = (0 ~eN times ~eL)
ndash 10 ndash
JHEP02(2012)045
where ~pminus and ~k are the three-momenta of the microminus and Klowast2 (1430) meson respectively in the
center mass (CM) frame of micro+microminus system Lorentz transformation is used to boost the
longitudinal component of the lepton polarization to the CM frame of the lepton pair as
(
sminusmicroL
)
CM=
( |~pminus|ml
El~pminusml |~pminus|
)
(314)
where El and ml are the energy and mass of the final state muon The normal and
transverse components remain unchanged under the Lorentz boost The longitudinal (PL)
normal (PN ) and transverse (PT ) polarizations of lepton can be defined as
P(∓)i (q2) =
dΓdq2
(~ξ∓ = ~e∓)minus dΓdq2
(~ξ∓ = minus~e∓)dΓdq2
(~ξ∓ = ~e∓) + dΓdq2
(~ξ∓ = minus~e∓)(315)
where i = L N T and ~ξ∓ is the spin direction along the leptons micro∓ The differential
decay rate for polarized lepton l∓ in B rarr Klowast2 (1430)micro
+microminus decay along any spin direction~ξ∓ is related to the unpolarized decay rate (36) with the following relation
dΓ(~ξ∓)
dq2=
1
2
(
dΓ
dq2
)
[1 + (P∓L ~e∓L + P∓
N~e∓N + P∓T ~e∓T ) middot ~ξ∓] (316)
We can achieve the expressions of longitudinal normal and transverse polarizations for
B rarr Klowast2 (1430)micro
+microminus decays as collected below The longitudinal lepton polarization can
be written as
PL prop1
36m2Bm
4T
4u(q2)radicλ[
P V AL + PSP
L + P TL
]
(317a)
P V AL = ml
(
2λF2 (F6 minusF7)m4B +
(
3λF1F5q2 + 2F2m
2B
(
10q2F6m2B + λF7
))
m2Klowast
2
+2λF3
(
F6
(
q2 minusm2B +m2
Klowast
2
)
m2B + λF7
))
(317b)
PSPL = 3mlλF9mB
(
minus2mlF8q2 minusF10mBq
2 + 2ml
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
(317c)
P TL = m2
lF11
(
24 (CTEF1 minus CTF5)m2Klowast
2λ+ 4CTλF3
(
m2B + 3m2
Klowast
2minus q2
)
+4m2B (4CTEF6 minus CTF2)
(
10(
m2B minusm2
Klowast
2
)
m2Klowast
2+ λ
))
+m2lF12
(
4m2B (4CTEF6 minus CTF2)
(
10q2m2Klowast
2+ λ
)
minus 4CTF3
(
q2 minusm2B +m2
Klowast
2
))
+m2lF13
(
2CTλminus 4CTF2m2B
(
m2B minusm2
Klowast
2minus q2
)
minus 2CTλ2F3
)
(317d)
ndash 11 ndash
JHEP02(2012)045
Similarly the normal lepton polarization is
PN prop minusπu(q2)t
(12m2Bm
4T
(λ
t)32
[
P V AN + PSP
N + P TN
]
(318a)
P V AN = 2ml
(
F2
(
F8q4 minus
(
(F6 minusF7 + F8)m2B + (minus3F1 + F7 minusF8)m
2Klowast
2
)
q2 (318b)
+(
m2B minusm2
Klowast
2
)
m2B
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
+ λF3
(
F8q2 minusF6m
2B + F7
(
m2B minusm2
Klowast
2
)))
PSPN = mBλ
(
F3F10q2 +
(
q2 minus 4m2l
)
F7F9
)
(318c)
minus(
F2F10q2 +
(
q2 minus 4m2l
)
F6F9
)
m3B
(
m2B minusm2
Klowast
2minus q2
)
P TN = F13
(
8m2l λCTE
(
F8q2 minusF6m
2B minusF7
(
m2Klowast
2minusm2
B
))
+ 4mlmBλCTEF10q2)
+F12
(
16m2lCTE
(
F6m2BminusF7
(
m2Bminusm2
Klowast
2
)
minusF8q2minusmB
2mlF10q
2
)
(
m2Bminusm2
Klowast
2minusq2
)
+ 6(
4m2l + q2
)
CTEF1q2m2
Klowast
2+ 3
(
q2 minus 4m2)
CTF5q2m2
Klowast
2
)
+F11
(
minus16m2lCTE
(
F8q2 + F7
(
m2B minusm2
Klowast
2
)
+mB
2mlF10q
2
)
(
m2B + 3m2
Klowast
2minus q2
)
+6m2Klowast
2
(
4m2l + q2
)
(
CTEF1
(
m2B minusm2
Klowast
2
)
minus CTF2m2B
)
+3(
4m2l minus q2
)
CTF5m2Klowast
2
(
m2Klowast
2minusm2
B
)
+4CTEF6m2B
(
4m2l
(
m2B + 6m2
Klowast
2minus q2
)
minus 3q2m2Klowast
2
)
)
(318d)
and the transverse one is given by
PT propiπλq2u(q2)
12mBm2Klowast
2
λCTEF13
(
4F2m2B minus 3F5m
2Klowast
2+ F3
(
q2 minus 5m2B +m2
Klowast
2
))
(319)
minus2F12
(
2CTE
((
8F3m2B minus (2F3 + 3F5)m
2Klowast
2
)
q2 + 4F2m2B
(
2m2B +m2
Klowast
2minus 2q2
)
minus(
m2Bminusm2
Klowast
2
)(
8F3m2B + (4F3 + 3F5)m
2Klowast
2
))
minus3CTF1m2Klowast
2
(
q2minus3m2B + 3m2
Klowast
2
))
+2F11
(
2CTE
(
3F5m2Klowast
2
(
3m2B +m2
Klowast
2minus q2
)
minus 4F2
(
2m2B + 3m2
Klowast
2minus 2q2
)
m2B
+2F3
(
7m2Klowast
2q2minus4q4+6λ+4m2
B
(
q2+5m2Klowast
2
)))
minus3CTF1m2Klowast
2
(
3m2B+m2
Klowast
2minusq2
)
34 Helicity fractions
Helicity fraction is an observable associated with polarization of the out going meson that
is almost free of hadronic uncertainties The spin-2 polarization tensor which satisfies
ǫmicroνkν = 0 with k being the momentum is symmetric and traceless It can be constructed
by the vector polarization ǫmicro as
ǫmicroν(plusmn2) = ǫmicro(plusmn)ǫν(plusmn) ǫmicroν(plusmn1) =1radic2[ǫmicro(plusmn)ǫν(0) + ǫmicro(0)ǫν(plusmn)]
ǫmicroν(0) =1radic6[ǫmicro(+)ǫν(minus) + ǫmicro(minus)ǫν(+)] +
radic
2
3ǫmicro(0)ǫν(0) (320)
ndash 12 ndash
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
In term of these operators the effective Hamiltonian for B rarr Klowast2 (1430)l
+lminus takes the
form
HSMeff = minusGFαradic
2πVtbV
lowastts
CSM9 (sγmicroPLb)(lγ
microl) + CSM10 (sγmicroPLb)(lγ
microγ5l)
minus2mbCSM7 (siσmicroν
qν
q2PRb)(lγ
microl)
(23)
where q2 is square of the sum of the momentum of final state leptons At the scale micro =
48GeV the SM Wilson coefficients takes the following values which are calculated at next-
to-next-to-leading order
Ceff7 = minus034 Ceff
9 = 4211 + Y (q2) C10 = minus4103 (24)
where Ceff7 = C7 minus C33minus 4C49minus 20C53minus 80C69 The function Y (q2) is given by
Y (z q2) = h(z q2)(3C1(micro) + C2(micro) + 3C3(micro) + C4(micro) + 3C5(micro) + C6(micro))
minus1
2h(1 sprime)(4C3(micro) + 4C4(micro) + 3C5(micro) + C6(micro))
minus1
2h(0 q2)(C3(micro) + 3C4(micro)) +
2
9(3C3(micro) + C4(micro) + 3C5(micro) + C6(micro)) (25)
with
h(z q2) = minus8
9lnz +
8
27+
4
9xminus 2
9(2 + x)|1minus x|12
ln∣
∣
∣
radic1minusx+1radic1minusxminus1
∣
∣
∣minus iπ for x equiv 4z2q2 lt 1
2 arctan 1radicxminus1
for x equiv 4z2q2 gt 1
h(0 q2) =8
27minus 8
9lnmb
microminus 4
9lnq2 +
4
9iπ (26)
and z = mcmb
22 New physics operators
The NP effects in semileptonic B meson decays can be established in two ways in one case
we can change the Wilson Coefficients but leave the operator basis same as that of the SM
and in other case we can add new operators too Here we do not restrict ourself to any
model and discuss all possible operators that corresponds to B rarr Klowast2 (1430)l
+lminus decays
In this scenario the total effective Hamiltonian for brarr sl+lminus can be written as
Heff = HSMeff +HV A
eff +HSPeff +HT
eff (27)
where HSMeff is given in eq (23) while [37]
HV Aeff =minus 4GFradic
2
α
4πV lowasttsVtb RV (sγmicroPLb) microγmicromicro+RA (sγmicroPLb) microγmicroγ5micro
+RprimeV (sγmicroPRb) microγmicromicro+Rprime
A (sγmicroPRb) microγmicroγ5micro
(28)
HSPeff =minus 4GFradic
2
α
4πV lowasttsVtb RS (sPRb) micromicro+RP (sPRb) microγ5micro
+RprimeS (sPLb) micromicro+Rprime
P (sPLb) microγ5micro
(29)
HTeff =minus 4GFradic
2
α
4πV lowasttsVtb
CT (sσmicroνb) microσmicroνmicro+ iCTE (sσmicroνb) microσαβmicroǫmicroναβ
(210)
ndash 4 ndash
JHEP02(2012)045
Here RV RA RV RprimeA RS RP R
primeS R
primeP CT and CTE are the NP effective couplings The
constraints on the numerical values of these NP coupling from different B meson decays
will be given later in this section
23 Parametrization of matrix elements and form factors
The exclusive B rarr Klowast2 (1430)l
+lminus decay involves the hadronic matrix elements of quark
operators which can be parameterized in terms of form factors These form factors are
written as
lang
Klowast2 (k ǫ) |sγmicrob|B(p)
rang
= minus 2V (q2)
mB +mKlowast
2
ǫmicroνρσεlowastναp
α
mBpρkσ (211)
lang
Klowast2 (k ǫ)
∣
∣sγmicroγ5b∣
∣B(p)rang
=2imKlowast
2A0(q
2)
q2εlowastναp
α
mBqνqmicro
+i(mB +mKlowast
2)A1(q
2)
mB
[
gmicroνεlowastναpα minus 1
q2εlowastναp
αqνqmicro]
minusiA2(q2)
εlowastναpαqν
mB(mB +mKlowast
2)
[
(pmicro + kmicro)minusm2
B minusm2Klowast
2
q2qmicro
]
(212)lang
Klowast2 (k ǫ) |sσmicroνqνb|B(p)
rang
= minus2iT1(q2)ǫmicroνρσ
εlowastναpα
mBpρkσ (213)
lang
Klowast2 (k ǫ)
∣
∣sσmicroνγ5qνb∣
∣B(p)rang
= T2(q2)[
(m2B minusm2
Klowast
2)gmicroνεlowastναp
α minus εlowastναpαqν(pmicro + kmicro)
] 1
mB
+T3(q2)εlowastναp
α
mBqν
[
qmicro minus q2
m2B minusm2
Klowast
2
(pmicro + kmicro)
]
(214)
lang
Klowast2 (k ǫ) |sb|B(p)
rang
=2V (q2)
(mB +mKlowast
2)(mb minusms)
ǫmicroνρσεlowastναp
α
mBpρkσ (215)
lang
Klowast2 (k ǫ)
∣
∣sγ5b∣
∣ B(p)rang
=2imKlowast
2A0(q
2)
q2εlowastναp
α
mB(mb +ms)qνqmicro (216)
lang
Klowast2 (k ǫ) |sσmicroνb|B(p)
rang
= minus2T1(q2)ǫmicroνρσ
εlowastναpα
mBpρkσ (217)
where p(k) is the momentum of the B(Klowast2 ) meson and εlowastνα is the polarization of the final
state Klowast2 (1430) meson In case of the tensor meson the polarization sum is given by [38]
Pmicroναβ =sum
εmicroν(p)εlowastαβ(p) =
1
2(θmicroαθνβ + θmicroβθνα)minus
1
3(θmicroνθαβ) (218)
with
θmicroν = minusgmicroν +kmicrokνm2
Klowast
2
(219)
Defining
εlowastν = εlowastναpαmB (220)
the resulting matrix elements for B rarr Klowast2 (1430) will look just like the B rarr V (eg Klowast
meson) transitions The form factors for B rarr Klowast2 (1430) transition are the non-perturbative
ndash 5 ndash
JHEP02(2012)045
F (q2) F (0) a b
V (q2) 016+002minus002 208 15
A0(q2) 025+004
minus004 157 01
A1(q2) 014+002
minus002 123 049
A2(q2) 005+002
minus002 132 149
T1(q2) 014+002
minus002 207 15
T2(q2) 014+002
minus002 122 034
T3(q2) 001+001
minus002 991 276
Table 1 B rarr Klowast
2 form factors in the light cone sum rules approach F (0) denotes the value
of form factors at q2 = 0 while a and b are the parameters in the parameterizations shown in
eq (221) [39]
quantities and are needed to be calculated using different approaches (both perturbative
and non-perturbative) like Lattice QCD QCD sum rules Light Cone sum rules etc Here
we will consider the form factors calculated in the LCSR approach [39] and their evolution
with q2 is given by
F (q2) =F (0)
1minus a(q2m2B) + b(q2m2
B)2
(221)
where the value of different parameters is given in table 1
The errors in the values of the form factors arise from number of input parameters
involved in their calculation in LCSR such as variations in the Boral parameters fluctuation
of threshold parameters errors in the b quark mass corrections from the decay constants
of involved mesons and from the Gengenbauer moments in the distribution amplitudes
It is worth mentioning here that it is possible to study this mode with the help of
QCD factorization which might discover additional sources of theoretical errors which are
overlooked in the simple form factor analysis As besides the factorizable contribution of
form factors which has been used here there are in principle non-factorizable contributions
to matrix elements as well [13] QCD factorization not only reduce the number of inde-
pendent parameters in heavy quark limit but also help us to compute the non-factorizable
corrections to B meson decays with the help of light-cone distribution amplitudes and
hard scattering kernel [53 54] The details of QCD factorization and its implications in
semileptonic and radiative B meson decays can be found in [13]
24 Numerical constraints on NP parameters
The constraints on NP parameters can be obtained from the branching ratios of B0s rarr
micro+microminus B0s rarr Xsmicro
+microminus and B0d rarr Kmicro+microminus [5 47ndash50] Due to the large hadronic uncertain-
ties the constraints obtained from the exclusive decay modes are somewhat weaker com-
pared to the inclusive ones The branching ratio of inclusive decay mode B rarr Xsmicro+microminus has
been measured by Babar [49] and Belle [50] and their measurements in low-q2 (1GeV2 le
ndash 6 ndash
JHEP02(2012)045
q2 le 6GeV2) and high-q2 (144GeV2 le q2 le 25GeV2) regions can be summarized as
B(B rarr Xsmicro+microminus)low q2 = (149plusmn 050+041
minus032)times 10minus6 (Belle)
(18plusmn 07plusmn 050)times 10minus6 (BaBar) (222)
(160plusmn 050)times 10minus6 (Average)
B(B rarr Xsmicro+microminus)high q2 = (042plusmn 012+007
minus007)times 10minus6 (Belle)
(050plusmn 025+007minus008)times 10minus6 (BaBar) (223)
(044plusmn 012)times 10minus6 (Average)
where q2 is the invariant mass squared of two muons and low-q2 region corresponds to
1GeV2 le q2 le 6GeV2 and high-q2 region corresponds to q2 ge 144GeV2
The constraints on the new V A couplings come mainly from B0d rarr Xsmicro
+microminus and B0d rarr
Kmicro+microminus [51] It has been shown in ref [51] that if RVA couplings are present only the
constraints on these couplings from above said decays came to be
10 le |RV + 36|2(47)2
+|RA minus 40|2
(48)2|RV + 28|2
(65)2+|RA minus 41|2
(66)2le 1 (224)
Similarly when we have only RprimeVA couplings the constraints on them from the same decay
will become [51]
22 le |RprimeV + 36|2 + |Rprime
A minus 40|2 le 566 |RprimeV |2 + |Rprime
A|2 le 17 (225)
These constraints are weekend when both RVA and RprimeVA couplings are present at the same
time In this case these new physics couplings are restricted to be
|RV + 28|2(65)2
+|RA minus 41|2
(66)2le 1 (226)
and
|RprimeV |2 + |Rprime
A|2 le 40 (227)
The limits on couplings corresponding to scalar-pseudoscalar (SP) operators comes
from the upper bound on B0s rarr micro+microminus which provides the limit
|RS minusRprimeS |2 + |RP minusRprime
P |2 le 044 (228)
This puts a sever constraint on the NP couplings if only RSP or RprimeSP are present However
under the condition where both types of operators are present RSP or RprimeSP these bounds
can be relaxed due to cancelation between the RSP and RprimeSP In this case B0
d rarr Xsmicro+microminus
and B0d rarr Kmicro+microminus can still bound these couplings and the stronger bound is obtained from
the measurement of later quantity which yields
|RS |2 + |RP |2 le 9 RS asymp RprimeS RS asymp Rprime
P (229)
Now the constraint on the NP tensor type couplings comes entirely from the inclusive
B0d rarr Xsmicro
+microminus decay In case when only tensor type operators are present the limits on
tensor type couplings are [51]
|CT |2 + |CTE |2 le 10 (230)
ndash 7 ndash
JHEP02(2012)045
In the present study we will examine B rarr Klowast2 (1430)micro
+microminus decays by using these NP
constraints
3 Decay rate forward-backward asymmetry and lepton polarization a-
symmetries for B rarr Klowast
2(1430)micro+microminus decay
In this section we are going to perform the calculations of some very interesting quantities
like the decay rate the forward-backward asymmetry the polarization asymmetries of
the final state lepton and the helicity fractions of the final state Klowast2 (1430) meson From
eq (27) it is straightforward to obtain the decay amplitude for B rarr Klowast2 (1430)micro
+microminus as
M(B rarr Klowast2 (1430)micro
+microminus) = minus GFα
2radic2π
VtbVlowastts
[
TmicroV lγmicrol + Tmicro
A lγmicroγ5l
+TS ll + TP lγ5l + Tmicroν
T lσmicroν l + iTmicroνE ǫmicroναβ lσαβl
]
(31)
with
TmicroV = minusF1ǫ
microναβεlowastνpKlowastαqβ + iF2εlowastmicro + iF3ε
lowast middot q(pB + pKlowast)micro + iF4εlowast middot qqmicro
TmicroA = minusF5ǫ
microναβεlowastνpKlowastαqβ + iF6εlowastmicro + iF7ε
lowast middot q(pB + pKlowast)micro + iF8εlowast middot qqmicro
TS = iF9εlowast middot q
TP = iF10εlowast middot pB
TmicroνT = CT
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
TmicroνE = CTE
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
(32)
The auxiliary functions F1 middot middot middot F13 appearing in eq (32) are defined as follows
F1 =
[
2V (q2)
mB +mKlowast
(Ceff9 +RV +Rprime
V ) +4mb
q2Ceff7 T1(q
2)
]
F2 = minus[
(mB +mKlowast)A1(q2)(Ceff
9 +RV minusRprimeV ) +
2mb
q2Ceff7 T1(q
2)(m2B minusmKlowast)
]
F3 =
[
A(q2)
mB +mKlowast
(Ceff9 +RV minusRprime
V ) +2mb
q2Ceff7
(
T1(q2) +
q2T3(q2)
m2B minusmKlowast
)]
F4 =
[
2mKlowast
q2(Ceff
9 +RV minusRprimeV )(A3(q
2)minusA0(q2))minus 2mb
q2Ceff7 T3(q
2)
]
F5 =
[
2V (q2)
mB +mKlowast
(Ceff10 +RA +Rprime
A)
]
F6 = minus[
(mB +mKlowast)A1(q2)(Ceff
10 +RA minusRprimeA)
]
F7 =
[
A(q2)
mB +mKlowast
(Ceff10 +RA minusRprime
A)
]
F8 =
[
2mKlowast
q2(Ceff
10 +RA minusRprimeA)(A3(q
2)minusA0(q2))
]
F9 =
[
minus2(RS minusRprimeS)
mKlowast
mbA0(q
2)
]
ndash 8 ndash
JHEP02(2012)045
F10 =
[
2(RP minusRprimeP )
mKlowast
mbA0(q
2)
]
F11 = minus2T1(q2)
F12 =
[
2(m2B minusm2
Klowast)
q2(T1(q
2)minus T2(q2))
]
F13 =
[
4
q2
(
T1(q2)minus T2(q
2)minus q2T3(q2)
m2B minusm2
Klowast
)]
(33)
31 Differential decay rate
The differential decay width of B rarr Klowast2 (1430)micro
+microminus in dilepton center of mass frame can
be written as
dΓ(B rarr Klowast2 (1430)micro
+microminus)
dq2=
1
(2π)31
32m3B
int u(q2)
minusu(q2)|MBrarrKlowast
2(1430)micro+microminus |2du (34)
where u = (p + pmicrominus)2 minus (p + pmicro+)2 = u(q2) cos θ and q2 = (pmicro+ + pmicrominus)2 p k pmicro+ and
pmicrominus are the four-momenta vectors of B Klowast2 (1430) micro
+ and microminus respectively and u(q2) are
given by
u(q2) =radic
m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2
radic
1minus 4m2l
q2(35)
Collecting everything together one can write the general expression of the differential decay
rate for B rarr Klowast2 (1430)micro
+microminus as
dΓ
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
18m2lm
4T q
2
3F21m
2Klowast
2q2λ+ 2F2
2m4B(λ+ 10m2
T q2) (36)
+2F23λ
2] (
2m2l + q2
)
minus[
3F25m
2Klowast
2minus 3F2
9m2B
]
K2q2λ+ 12F2
8m2l q
4λ
+2F26m
4B
[
2(
λminus 20m2T q
2)
m2l + q2
(
λ+ 10m2T q
2)]
+ 3F210m
2Bq
4λ
+2F27λ
[
2(
λminus 3q4 + 6m2T q
2)
m2Klowast
2+ q2λ
]
minus 4F2F3m4B
(
2m2l + q2
)
K1λ2
minus4F6F7m2Bλ
[
2(
K1 + 3q2)
m2l +K1q
2]
minus 24F6F8m2lm
2Bq
2λminus 12F10F6mlm3Bq
2λ
+24F7F8m2lK0q
2λ+ 12F10F7mlmBK0q2λ+ 8F11F12q
2(λ+ 10m2Tm
2B minus 10m4
T )K3
minus4F11F13(K1 + 4m2T )λq
2K3 minus 72F1F11mlm2Klowast
2q2λCT
+48F11F2mlm2Bq
2(λ+ 10m2Tm
2B minus 10m4
T )CTE minus 4F12F13K1λq2K3
+48F12F2mlm2Bq
2(
λ+ 10m2T q
2)
CTE minus 48F12F3mlq2K1CTEλ
minus24F13F2mlm2BK1λq
2CTE + 24F13F3mlq2CTEλ
2
where ml is the mass of final state muon and
λ = λ(
m2Bm
2Klowast
2 q2
)
equiv m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2 (37)
K0 = (m2B minusm2
Klowast
2) K1 =
(
m2B minusm2
Klowast
2minus q2
)
K2 = q2 minus 4m2l
K3 = q2C2T minus 4m2
l
(
C2T minus 36C2
TE
)
(38)
and the auxiliary functions are the same as defined in eq (33)
ndash 9 ndash
JHEP02(2012)045
32 Forward-backward asymmetry
Now we are in a position to explore the forward-backward asymmetry of final state leptons
in the B rarr Klowast2 (1430)micro
+microminus which is an essential observable sensitive to the new physics
effects To calculate the forward-backward asymmetry we consider the following double
differential decay rate formula for the process B rarr Klowast2 (1430)micro
+microminus
d2Γ(q2 cos θ)
dq2d cos θ=
1
(2π)31
64m3B
u(q2)|MBrarrKlowast
2(1430)micro+microminus |2 (39)
where θ is the angle between the momentum of B baryon and lminus in the dilepton rest frame
The differential and normalized FBAs for the semi-leptonic decay B rarr Klowast2 (1430)l
+lminus are
defined as
dAFB(q2)
dq2=
int 1
0d cos θ
d2Γ(q2 cos θ)
dq2d cos θminusint 0
minus1d cos θ
d2Γ(q2 cos θ)
dq2d cos θ(310)
and
AFB(q2) =
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θminusint 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θ+int 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
(311)
Following the same procedure as we did for the differential decay rate one can easily get
the expression for the forward-backward asymmetry as follows
dAFB(q2)
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
6mBm4T
[
AV AFB +ASP
FB +ATSPFB +AT
FB
]
(312a)
AV AFB = minus3(F2F5 + F1F6)q
2m2Bm
2K2
(312b)
ASPFB = 2F9mlmB
(
F3λ+ F2m2B
[
q2 minusm2B +m2
K2
])
(312c)
ATSPFB = minusq2 (F10CT + 2F9CTE)mB
(
2F12
(
m2B minusm2
K2minus q2
)
(312d)
minusF13λ+ 2F11
(
m2B + 3m2
K2minus q2
))
ATFB = minus2ml
(
12F12F5q2CTEm
2K2
+ 12F11F5CTEm2K2
(
m2B minusm2
K2
)
(312e)
+F13λCT
(
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F12CT
(
m2B minusm2
K2minus q2
) (
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F11CT
(
F6m2B
(
m2B + 9m2
K2minus q2
)
minus(
m2B + 3m2
K2minus q2
) (
F8q2 + F7
(
m2B minusm2
K2
)))
and the expression of the differential decay rate is given in eq (36)
33 Lepton polarization asymmetries
In the rest frame of the lepton microminus the unit vectors along longitudinal normal and transver-
sal component of the microminus can be defined as [55]
sminusmicroL = (0 ~eL) =
(
0~pminus|~pminus|
)
sminusmicroN = (0 ~eN ) =
0~k times ~pminus∣
∣
∣
~k times ~pminus∣
∣
∣
(313)
sminusmicroT = (0 ~eT ) = (0 ~eN times ~eL)
ndash 10 ndash
JHEP02(2012)045
where ~pminus and ~k are the three-momenta of the microminus and Klowast2 (1430) meson respectively in the
center mass (CM) frame of micro+microminus system Lorentz transformation is used to boost the
longitudinal component of the lepton polarization to the CM frame of the lepton pair as
(
sminusmicroL
)
CM=
( |~pminus|ml
El~pminusml |~pminus|
)
(314)
where El and ml are the energy and mass of the final state muon The normal and
transverse components remain unchanged under the Lorentz boost The longitudinal (PL)
normal (PN ) and transverse (PT ) polarizations of lepton can be defined as
P(∓)i (q2) =
dΓdq2
(~ξ∓ = ~e∓)minus dΓdq2
(~ξ∓ = minus~e∓)dΓdq2
(~ξ∓ = ~e∓) + dΓdq2
(~ξ∓ = minus~e∓)(315)
where i = L N T and ~ξ∓ is the spin direction along the leptons micro∓ The differential
decay rate for polarized lepton l∓ in B rarr Klowast2 (1430)micro
+microminus decay along any spin direction~ξ∓ is related to the unpolarized decay rate (36) with the following relation
dΓ(~ξ∓)
dq2=
1
2
(
dΓ
dq2
)
[1 + (P∓L ~e∓L + P∓
N~e∓N + P∓T ~e∓T ) middot ~ξ∓] (316)
We can achieve the expressions of longitudinal normal and transverse polarizations for
B rarr Klowast2 (1430)micro
+microminus decays as collected below The longitudinal lepton polarization can
be written as
PL prop1
36m2Bm
4T
4u(q2)radicλ[
P V AL + PSP
L + P TL
]
(317a)
P V AL = ml
(
2λF2 (F6 minusF7)m4B +
(
3λF1F5q2 + 2F2m
2B
(
10q2F6m2B + λF7
))
m2Klowast
2
+2λF3
(
F6
(
q2 minusm2B +m2
Klowast
2
)
m2B + λF7
))
(317b)
PSPL = 3mlλF9mB
(
minus2mlF8q2 minusF10mBq
2 + 2ml
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
(317c)
P TL = m2
lF11
(
24 (CTEF1 minus CTF5)m2Klowast
2λ+ 4CTλF3
(
m2B + 3m2
Klowast
2minus q2
)
+4m2B (4CTEF6 minus CTF2)
(
10(
m2B minusm2
Klowast
2
)
m2Klowast
2+ λ
))
+m2lF12
(
4m2B (4CTEF6 minus CTF2)
(
10q2m2Klowast
2+ λ
)
minus 4CTF3
(
q2 minusm2B +m2
Klowast
2
))
+m2lF13
(
2CTλminus 4CTF2m2B
(
m2B minusm2
Klowast
2minus q2
)
minus 2CTλ2F3
)
(317d)
ndash 11 ndash
JHEP02(2012)045
Similarly the normal lepton polarization is
PN prop minusπu(q2)t
(12m2Bm
4T
(λ
t)32
[
P V AN + PSP
N + P TN
]
(318a)
P V AN = 2ml
(
F2
(
F8q4 minus
(
(F6 minusF7 + F8)m2B + (minus3F1 + F7 minusF8)m
2Klowast
2
)
q2 (318b)
+(
m2B minusm2
Klowast
2
)
m2B
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
+ λF3
(
F8q2 minusF6m
2B + F7
(
m2B minusm2
Klowast
2
)))
PSPN = mBλ
(
F3F10q2 +
(
q2 minus 4m2l
)
F7F9
)
(318c)
minus(
F2F10q2 +
(
q2 minus 4m2l
)
F6F9
)
m3B
(
m2B minusm2
Klowast
2minus q2
)
P TN = F13
(
8m2l λCTE
(
F8q2 minusF6m
2B minusF7
(
m2Klowast
2minusm2
B
))
+ 4mlmBλCTEF10q2)
+F12
(
16m2lCTE
(
F6m2BminusF7
(
m2Bminusm2
Klowast
2
)
minusF8q2minusmB
2mlF10q
2
)
(
m2Bminusm2
Klowast
2minusq2
)
+ 6(
4m2l + q2
)
CTEF1q2m2
Klowast
2+ 3
(
q2 minus 4m2)
CTF5q2m2
Klowast
2
)
+F11
(
minus16m2lCTE
(
F8q2 + F7
(
m2B minusm2
Klowast
2
)
+mB
2mlF10q
2
)
(
m2B + 3m2
Klowast
2minus q2
)
+6m2Klowast
2
(
4m2l + q2
)
(
CTEF1
(
m2B minusm2
Klowast
2
)
minus CTF2m2B
)
+3(
4m2l minus q2
)
CTF5m2Klowast
2
(
m2Klowast
2minusm2
B
)
+4CTEF6m2B
(
4m2l
(
m2B + 6m2
Klowast
2minus q2
)
minus 3q2m2Klowast
2
)
)
(318d)
and the transverse one is given by
PT propiπλq2u(q2)
12mBm2Klowast
2
λCTEF13
(
4F2m2B minus 3F5m
2Klowast
2+ F3
(
q2 minus 5m2B +m2
Klowast
2
))
(319)
minus2F12
(
2CTE
((
8F3m2B minus (2F3 + 3F5)m
2Klowast
2
)
q2 + 4F2m2B
(
2m2B +m2
Klowast
2minus 2q2
)
minus(
m2Bminusm2
Klowast
2
)(
8F3m2B + (4F3 + 3F5)m
2Klowast
2
))
minus3CTF1m2Klowast
2
(
q2minus3m2B + 3m2
Klowast
2
))
+2F11
(
2CTE
(
3F5m2Klowast
2
(
3m2B +m2
Klowast
2minus q2
)
minus 4F2
(
2m2B + 3m2
Klowast
2minus 2q2
)
m2B
+2F3
(
7m2Klowast
2q2minus4q4+6λ+4m2
B
(
q2+5m2Klowast
2
)))
minus3CTF1m2Klowast
2
(
3m2B+m2
Klowast
2minusq2
)
34 Helicity fractions
Helicity fraction is an observable associated with polarization of the out going meson that
is almost free of hadronic uncertainties The spin-2 polarization tensor which satisfies
ǫmicroνkν = 0 with k being the momentum is symmetric and traceless It can be constructed
by the vector polarization ǫmicro as
ǫmicroν(plusmn2) = ǫmicro(plusmn)ǫν(plusmn) ǫmicroν(plusmn1) =1radic2[ǫmicro(plusmn)ǫν(0) + ǫmicro(0)ǫν(plusmn)]
ǫmicroν(0) =1radic6[ǫmicro(+)ǫν(minus) + ǫmicro(minus)ǫν(+)] +
radic
2
3ǫmicro(0)ǫν(0) (320)
ndash 12 ndash
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
Here RV RA RV RprimeA RS RP R
primeS R
primeP CT and CTE are the NP effective couplings The
constraints on the numerical values of these NP coupling from different B meson decays
will be given later in this section
23 Parametrization of matrix elements and form factors
The exclusive B rarr Klowast2 (1430)l
+lminus decay involves the hadronic matrix elements of quark
operators which can be parameterized in terms of form factors These form factors are
written as
lang
Klowast2 (k ǫ) |sγmicrob|B(p)
rang
= minus 2V (q2)
mB +mKlowast
2
ǫmicroνρσεlowastναp
α
mBpρkσ (211)
lang
Klowast2 (k ǫ)
∣
∣sγmicroγ5b∣
∣B(p)rang
=2imKlowast
2A0(q
2)
q2εlowastναp
α
mBqνqmicro
+i(mB +mKlowast
2)A1(q
2)
mB
[
gmicroνεlowastναpα minus 1
q2εlowastναp
αqνqmicro]
minusiA2(q2)
εlowastναpαqν
mB(mB +mKlowast
2)
[
(pmicro + kmicro)minusm2
B minusm2Klowast
2
q2qmicro
]
(212)lang
Klowast2 (k ǫ) |sσmicroνqνb|B(p)
rang
= minus2iT1(q2)ǫmicroνρσ
εlowastναpα
mBpρkσ (213)
lang
Klowast2 (k ǫ)
∣
∣sσmicroνγ5qνb∣
∣B(p)rang
= T2(q2)[
(m2B minusm2
Klowast
2)gmicroνεlowastναp
α minus εlowastναpαqν(pmicro + kmicro)
] 1
mB
+T3(q2)εlowastναp
α
mBqν
[
qmicro minus q2
m2B minusm2
Klowast
2
(pmicro + kmicro)
]
(214)
lang
Klowast2 (k ǫ) |sb|B(p)
rang
=2V (q2)
(mB +mKlowast
2)(mb minusms)
ǫmicroνρσεlowastναp
α
mBpρkσ (215)
lang
Klowast2 (k ǫ)
∣
∣sγ5b∣
∣ B(p)rang
=2imKlowast
2A0(q
2)
q2εlowastναp
α
mB(mb +ms)qνqmicro (216)
lang
Klowast2 (k ǫ) |sσmicroνb|B(p)
rang
= minus2T1(q2)ǫmicroνρσ
εlowastναpα
mBpρkσ (217)
where p(k) is the momentum of the B(Klowast2 ) meson and εlowastνα is the polarization of the final
state Klowast2 (1430) meson In case of the tensor meson the polarization sum is given by [38]
Pmicroναβ =sum
εmicroν(p)εlowastαβ(p) =
1
2(θmicroαθνβ + θmicroβθνα)minus
1
3(θmicroνθαβ) (218)
with
θmicroν = minusgmicroν +kmicrokνm2
Klowast
2
(219)
Defining
εlowastν = εlowastναpαmB (220)
the resulting matrix elements for B rarr Klowast2 (1430) will look just like the B rarr V (eg Klowast
meson) transitions The form factors for B rarr Klowast2 (1430) transition are the non-perturbative
ndash 5 ndash
JHEP02(2012)045
F (q2) F (0) a b
V (q2) 016+002minus002 208 15
A0(q2) 025+004
minus004 157 01
A1(q2) 014+002
minus002 123 049
A2(q2) 005+002
minus002 132 149
T1(q2) 014+002
minus002 207 15
T2(q2) 014+002
minus002 122 034
T3(q2) 001+001
minus002 991 276
Table 1 B rarr Klowast
2 form factors in the light cone sum rules approach F (0) denotes the value
of form factors at q2 = 0 while a and b are the parameters in the parameterizations shown in
eq (221) [39]
quantities and are needed to be calculated using different approaches (both perturbative
and non-perturbative) like Lattice QCD QCD sum rules Light Cone sum rules etc Here
we will consider the form factors calculated in the LCSR approach [39] and their evolution
with q2 is given by
F (q2) =F (0)
1minus a(q2m2B) + b(q2m2
B)2
(221)
where the value of different parameters is given in table 1
The errors in the values of the form factors arise from number of input parameters
involved in their calculation in LCSR such as variations in the Boral parameters fluctuation
of threshold parameters errors in the b quark mass corrections from the decay constants
of involved mesons and from the Gengenbauer moments in the distribution amplitudes
It is worth mentioning here that it is possible to study this mode with the help of
QCD factorization which might discover additional sources of theoretical errors which are
overlooked in the simple form factor analysis As besides the factorizable contribution of
form factors which has been used here there are in principle non-factorizable contributions
to matrix elements as well [13] QCD factorization not only reduce the number of inde-
pendent parameters in heavy quark limit but also help us to compute the non-factorizable
corrections to B meson decays with the help of light-cone distribution amplitudes and
hard scattering kernel [53 54] The details of QCD factorization and its implications in
semileptonic and radiative B meson decays can be found in [13]
24 Numerical constraints on NP parameters
The constraints on NP parameters can be obtained from the branching ratios of B0s rarr
micro+microminus B0s rarr Xsmicro
+microminus and B0d rarr Kmicro+microminus [5 47ndash50] Due to the large hadronic uncertain-
ties the constraints obtained from the exclusive decay modes are somewhat weaker com-
pared to the inclusive ones The branching ratio of inclusive decay mode B rarr Xsmicro+microminus has
been measured by Babar [49] and Belle [50] and their measurements in low-q2 (1GeV2 le
ndash 6 ndash
JHEP02(2012)045
q2 le 6GeV2) and high-q2 (144GeV2 le q2 le 25GeV2) regions can be summarized as
B(B rarr Xsmicro+microminus)low q2 = (149plusmn 050+041
minus032)times 10minus6 (Belle)
(18plusmn 07plusmn 050)times 10minus6 (BaBar) (222)
(160plusmn 050)times 10minus6 (Average)
B(B rarr Xsmicro+microminus)high q2 = (042plusmn 012+007
minus007)times 10minus6 (Belle)
(050plusmn 025+007minus008)times 10minus6 (BaBar) (223)
(044plusmn 012)times 10minus6 (Average)
where q2 is the invariant mass squared of two muons and low-q2 region corresponds to
1GeV2 le q2 le 6GeV2 and high-q2 region corresponds to q2 ge 144GeV2
The constraints on the new V A couplings come mainly from B0d rarr Xsmicro
+microminus and B0d rarr
Kmicro+microminus [51] It has been shown in ref [51] that if RVA couplings are present only the
constraints on these couplings from above said decays came to be
10 le |RV + 36|2(47)2
+|RA minus 40|2
(48)2|RV + 28|2
(65)2+|RA minus 41|2
(66)2le 1 (224)
Similarly when we have only RprimeVA couplings the constraints on them from the same decay
will become [51]
22 le |RprimeV + 36|2 + |Rprime
A minus 40|2 le 566 |RprimeV |2 + |Rprime
A|2 le 17 (225)
These constraints are weekend when both RVA and RprimeVA couplings are present at the same
time In this case these new physics couplings are restricted to be
|RV + 28|2(65)2
+|RA minus 41|2
(66)2le 1 (226)
and
|RprimeV |2 + |Rprime
A|2 le 40 (227)
The limits on couplings corresponding to scalar-pseudoscalar (SP) operators comes
from the upper bound on B0s rarr micro+microminus which provides the limit
|RS minusRprimeS |2 + |RP minusRprime
P |2 le 044 (228)
This puts a sever constraint on the NP couplings if only RSP or RprimeSP are present However
under the condition where both types of operators are present RSP or RprimeSP these bounds
can be relaxed due to cancelation between the RSP and RprimeSP In this case B0
d rarr Xsmicro+microminus
and B0d rarr Kmicro+microminus can still bound these couplings and the stronger bound is obtained from
the measurement of later quantity which yields
|RS |2 + |RP |2 le 9 RS asymp RprimeS RS asymp Rprime
P (229)
Now the constraint on the NP tensor type couplings comes entirely from the inclusive
B0d rarr Xsmicro
+microminus decay In case when only tensor type operators are present the limits on
tensor type couplings are [51]
|CT |2 + |CTE |2 le 10 (230)
ndash 7 ndash
JHEP02(2012)045
In the present study we will examine B rarr Klowast2 (1430)micro
+microminus decays by using these NP
constraints
3 Decay rate forward-backward asymmetry and lepton polarization a-
symmetries for B rarr Klowast
2(1430)micro+microminus decay
In this section we are going to perform the calculations of some very interesting quantities
like the decay rate the forward-backward asymmetry the polarization asymmetries of
the final state lepton and the helicity fractions of the final state Klowast2 (1430) meson From
eq (27) it is straightforward to obtain the decay amplitude for B rarr Klowast2 (1430)micro
+microminus as
M(B rarr Klowast2 (1430)micro
+microminus) = minus GFα
2radic2π
VtbVlowastts
[
TmicroV lγmicrol + Tmicro
A lγmicroγ5l
+TS ll + TP lγ5l + Tmicroν
T lσmicroν l + iTmicroνE ǫmicroναβ lσαβl
]
(31)
with
TmicroV = minusF1ǫ
microναβεlowastνpKlowastαqβ + iF2εlowastmicro + iF3ε
lowast middot q(pB + pKlowast)micro + iF4εlowast middot qqmicro
TmicroA = minusF5ǫ
microναβεlowastνpKlowastαqβ + iF6εlowastmicro + iF7ε
lowast middot q(pB + pKlowast)micro + iF8εlowast middot qqmicro
TS = iF9εlowast middot q
TP = iF10εlowast middot pB
TmicroνT = CT
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
TmicroνE = CTE
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
(32)
The auxiliary functions F1 middot middot middot F13 appearing in eq (32) are defined as follows
F1 =
[
2V (q2)
mB +mKlowast
(Ceff9 +RV +Rprime
V ) +4mb
q2Ceff7 T1(q
2)
]
F2 = minus[
(mB +mKlowast)A1(q2)(Ceff
9 +RV minusRprimeV ) +
2mb
q2Ceff7 T1(q
2)(m2B minusmKlowast)
]
F3 =
[
A(q2)
mB +mKlowast
(Ceff9 +RV minusRprime
V ) +2mb
q2Ceff7
(
T1(q2) +
q2T3(q2)
m2B minusmKlowast
)]
F4 =
[
2mKlowast
q2(Ceff
9 +RV minusRprimeV )(A3(q
2)minusA0(q2))minus 2mb
q2Ceff7 T3(q
2)
]
F5 =
[
2V (q2)
mB +mKlowast
(Ceff10 +RA +Rprime
A)
]
F6 = minus[
(mB +mKlowast)A1(q2)(Ceff
10 +RA minusRprimeA)
]
F7 =
[
A(q2)
mB +mKlowast
(Ceff10 +RA minusRprime
A)
]
F8 =
[
2mKlowast
q2(Ceff
10 +RA minusRprimeA)(A3(q
2)minusA0(q2))
]
F9 =
[
minus2(RS minusRprimeS)
mKlowast
mbA0(q
2)
]
ndash 8 ndash
JHEP02(2012)045
F10 =
[
2(RP minusRprimeP )
mKlowast
mbA0(q
2)
]
F11 = minus2T1(q2)
F12 =
[
2(m2B minusm2
Klowast)
q2(T1(q
2)minus T2(q2))
]
F13 =
[
4
q2
(
T1(q2)minus T2(q
2)minus q2T3(q2)
m2B minusm2
Klowast
)]
(33)
31 Differential decay rate
The differential decay width of B rarr Klowast2 (1430)micro
+microminus in dilepton center of mass frame can
be written as
dΓ(B rarr Klowast2 (1430)micro
+microminus)
dq2=
1
(2π)31
32m3B
int u(q2)
minusu(q2)|MBrarrKlowast
2(1430)micro+microminus |2du (34)
where u = (p + pmicrominus)2 minus (p + pmicro+)2 = u(q2) cos θ and q2 = (pmicro+ + pmicrominus)2 p k pmicro+ and
pmicrominus are the four-momenta vectors of B Klowast2 (1430) micro
+ and microminus respectively and u(q2) are
given by
u(q2) =radic
m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2
radic
1minus 4m2l
q2(35)
Collecting everything together one can write the general expression of the differential decay
rate for B rarr Klowast2 (1430)micro
+microminus as
dΓ
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
18m2lm
4T q
2
3F21m
2Klowast
2q2λ+ 2F2
2m4B(λ+ 10m2
T q2) (36)
+2F23λ
2] (
2m2l + q2
)
minus[
3F25m
2Klowast
2minus 3F2
9m2B
]
K2q2λ+ 12F2
8m2l q
4λ
+2F26m
4B
[
2(
λminus 20m2T q
2)
m2l + q2
(
λ+ 10m2T q
2)]
+ 3F210m
2Bq
4λ
+2F27λ
[
2(
λminus 3q4 + 6m2T q
2)
m2Klowast
2+ q2λ
]
minus 4F2F3m4B
(
2m2l + q2
)
K1λ2
minus4F6F7m2Bλ
[
2(
K1 + 3q2)
m2l +K1q
2]
minus 24F6F8m2lm
2Bq
2λminus 12F10F6mlm3Bq
2λ
+24F7F8m2lK0q
2λ+ 12F10F7mlmBK0q2λ+ 8F11F12q
2(λ+ 10m2Tm
2B minus 10m4
T )K3
minus4F11F13(K1 + 4m2T )λq
2K3 minus 72F1F11mlm2Klowast
2q2λCT
+48F11F2mlm2Bq
2(λ+ 10m2Tm
2B minus 10m4
T )CTE minus 4F12F13K1λq2K3
+48F12F2mlm2Bq
2(
λ+ 10m2T q
2)
CTE minus 48F12F3mlq2K1CTEλ
minus24F13F2mlm2BK1λq
2CTE + 24F13F3mlq2CTEλ
2
where ml is the mass of final state muon and
λ = λ(
m2Bm
2Klowast
2 q2
)
equiv m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2 (37)
K0 = (m2B minusm2
Klowast
2) K1 =
(
m2B minusm2
Klowast
2minus q2
)
K2 = q2 minus 4m2l
K3 = q2C2T minus 4m2
l
(
C2T minus 36C2
TE
)
(38)
and the auxiliary functions are the same as defined in eq (33)
ndash 9 ndash
JHEP02(2012)045
32 Forward-backward asymmetry
Now we are in a position to explore the forward-backward asymmetry of final state leptons
in the B rarr Klowast2 (1430)micro
+microminus which is an essential observable sensitive to the new physics
effects To calculate the forward-backward asymmetry we consider the following double
differential decay rate formula for the process B rarr Klowast2 (1430)micro
+microminus
d2Γ(q2 cos θ)
dq2d cos θ=
1
(2π)31
64m3B
u(q2)|MBrarrKlowast
2(1430)micro+microminus |2 (39)
where θ is the angle between the momentum of B baryon and lminus in the dilepton rest frame
The differential and normalized FBAs for the semi-leptonic decay B rarr Klowast2 (1430)l
+lminus are
defined as
dAFB(q2)
dq2=
int 1
0d cos θ
d2Γ(q2 cos θ)
dq2d cos θminusint 0
minus1d cos θ
d2Γ(q2 cos θ)
dq2d cos θ(310)
and
AFB(q2) =
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θminusint 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θ+int 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
(311)
Following the same procedure as we did for the differential decay rate one can easily get
the expression for the forward-backward asymmetry as follows
dAFB(q2)
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
6mBm4T
[
AV AFB +ASP
FB +ATSPFB +AT
FB
]
(312a)
AV AFB = minus3(F2F5 + F1F6)q
2m2Bm
2K2
(312b)
ASPFB = 2F9mlmB
(
F3λ+ F2m2B
[
q2 minusm2B +m2
K2
])
(312c)
ATSPFB = minusq2 (F10CT + 2F9CTE)mB
(
2F12
(
m2B minusm2
K2minus q2
)
(312d)
minusF13λ+ 2F11
(
m2B + 3m2
K2minus q2
))
ATFB = minus2ml
(
12F12F5q2CTEm
2K2
+ 12F11F5CTEm2K2
(
m2B minusm2
K2
)
(312e)
+F13λCT
(
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F12CT
(
m2B minusm2
K2minus q2
) (
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F11CT
(
F6m2B
(
m2B + 9m2
K2minus q2
)
minus(
m2B + 3m2
K2minus q2
) (
F8q2 + F7
(
m2B minusm2
K2
)))
and the expression of the differential decay rate is given in eq (36)
33 Lepton polarization asymmetries
In the rest frame of the lepton microminus the unit vectors along longitudinal normal and transver-
sal component of the microminus can be defined as [55]
sminusmicroL = (0 ~eL) =
(
0~pminus|~pminus|
)
sminusmicroN = (0 ~eN ) =
0~k times ~pminus∣
∣
∣
~k times ~pminus∣
∣
∣
(313)
sminusmicroT = (0 ~eT ) = (0 ~eN times ~eL)
ndash 10 ndash
JHEP02(2012)045
where ~pminus and ~k are the three-momenta of the microminus and Klowast2 (1430) meson respectively in the
center mass (CM) frame of micro+microminus system Lorentz transformation is used to boost the
longitudinal component of the lepton polarization to the CM frame of the lepton pair as
(
sminusmicroL
)
CM=
( |~pminus|ml
El~pminusml |~pminus|
)
(314)
where El and ml are the energy and mass of the final state muon The normal and
transverse components remain unchanged under the Lorentz boost The longitudinal (PL)
normal (PN ) and transverse (PT ) polarizations of lepton can be defined as
P(∓)i (q2) =
dΓdq2
(~ξ∓ = ~e∓)minus dΓdq2
(~ξ∓ = minus~e∓)dΓdq2
(~ξ∓ = ~e∓) + dΓdq2
(~ξ∓ = minus~e∓)(315)
where i = L N T and ~ξ∓ is the spin direction along the leptons micro∓ The differential
decay rate for polarized lepton l∓ in B rarr Klowast2 (1430)micro
+microminus decay along any spin direction~ξ∓ is related to the unpolarized decay rate (36) with the following relation
dΓ(~ξ∓)
dq2=
1
2
(
dΓ
dq2
)
[1 + (P∓L ~e∓L + P∓
N~e∓N + P∓T ~e∓T ) middot ~ξ∓] (316)
We can achieve the expressions of longitudinal normal and transverse polarizations for
B rarr Klowast2 (1430)micro
+microminus decays as collected below The longitudinal lepton polarization can
be written as
PL prop1
36m2Bm
4T
4u(q2)radicλ[
P V AL + PSP
L + P TL
]
(317a)
P V AL = ml
(
2λF2 (F6 minusF7)m4B +
(
3λF1F5q2 + 2F2m
2B
(
10q2F6m2B + λF7
))
m2Klowast
2
+2λF3
(
F6
(
q2 minusm2B +m2
Klowast
2
)
m2B + λF7
))
(317b)
PSPL = 3mlλF9mB
(
minus2mlF8q2 minusF10mBq
2 + 2ml
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
(317c)
P TL = m2
lF11
(
24 (CTEF1 minus CTF5)m2Klowast
2λ+ 4CTλF3
(
m2B + 3m2
Klowast
2minus q2
)
+4m2B (4CTEF6 minus CTF2)
(
10(
m2B minusm2
Klowast
2
)
m2Klowast
2+ λ
))
+m2lF12
(
4m2B (4CTEF6 minus CTF2)
(
10q2m2Klowast
2+ λ
)
minus 4CTF3
(
q2 minusm2B +m2
Klowast
2
))
+m2lF13
(
2CTλminus 4CTF2m2B
(
m2B minusm2
Klowast
2minus q2
)
minus 2CTλ2F3
)
(317d)
ndash 11 ndash
JHEP02(2012)045
Similarly the normal lepton polarization is
PN prop minusπu(q2)t
(12m2Bm
4T
(λ
t)32
[
P V AN + PSP
N + P TN
]
(318a)
P V AN = 2ml
(
F2
(
F8q4 minus
(
(F6 minusF7 + F8)m2B + (minus3F1 + F7 minusF8)m
2Klowast
2
)
q2 (318b)
+(
m2B minusm2
Klowast
2
)
m2B
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
+ λF3
(
F8q2 minusF6m
2B + F7
(
m2B minusm2
Klowast
2
)))
PSPN = mBλ
(
F3F10q2 +
(
q2 minus 4m2l
)
F7F9
)
(318c)
minus(
F2F10q2 +
(
q2 minus 4m2l
)
F6F9
)
m3B
(
m2B minusm2
Klowast
2minus q2
)
P TN = F13
(
8m2l λCTE
(
F8q2 minusF6m
2B minusF7
(
m2Klowast
2minusm2
B
))
+ 4mlmBλCTEF10q2)
+F12
(
16m2lCTE
(
F6m2BminusF7
(
m2Bminusm2
Klowast
2
)
minusF8q2minusmB
2mlF10q
2
)
(
m2Bminusm2
Klowast
2minusq2
)
+ 6(
4m2l + q2
)
CTEF1q2m2
Klowast
2+ 3
(
q2 minus 4m2)
CTF5q2m2
Klowast
2
)
+F11
(
minus16m2lCTE
(
F8q2 + F7
(
m2B minusm2
Klowast
2
)
+mB
2mlF10q
2
)
(
m2B + 3m2
Klowast
2minus q2
)
+6m2Klowast
2
(
4m2l + q2
)
(
CTEF1
(
m2B minusm2
Klowast
2
)
minus CTF2m2B
)
+3(
4m2l minus q2
)
CTF5m2Klowast
2
(
m2Klowast
2minusm2
B
)
+4CTEF6m2B
(
4m2l
(
m2B + 6m2
Klowast
2minus q2
)
minus 3q2m2Klowast
2
)
)
(318d)
and the transverse one is given by
PT propiπλq2u(q2)
12mBm2Klowast
2
λCTEF13
(
4F2m2B minus 3F5m
2Klowast
2+ F3
(
q2 minus 5m2B +m2
Klowast
2
))
(319)
minus2F12
(
2CTE
((
8F3m2B minus (2F3 + 3F5)m
2Klowast
2
)
q2 + 4F2m2B
(
2m2B +m2
Klowast
2minus 2q2
)
minus(
m2Bminusm2
Klowast
2
)(
8F3m2B + (4F3 + 3F5)m
2Klowast
2
))
minus3CTF1m2Klowast
2
(
q2minus3m2B + 3m2
Klowast
2
))
+2F11
(
2CTE
(
3F5m2Klowast
2
(
3m2B +m2
Klowast
2minus q2
)
minus 4F2
(
2m2B + 3m2
Klowast
2minus 2q2
)
m2B
+2F3
(
7m2Klowast
2q2minus4q4+6λ+4m2
B
(
q2+5m2Klowast
2
)))
minus3CTF1m2Klowast
2
(
3m2B+m2
Klowast
2minusq2
)
34 Helicity fractions
Helicity fraction is an observable associated with polarization of the out going meson that
is almost free of hadronic uncertainties The spin-2 polarization tensor which satisfies
ǫmicroνkν = 0 with k being the momentum is symmetric and traceless It can be constructed
by the vector polarization ǫmicro as
ǫmicroν(plusmn2) = ǫmicro(plusmn)ǫν(plusmn) ǫmicroν(plusmn1) =1radic2[ǫmicro(plusmn)ǫν(0) + ǫmicro(0)ǫν(plusmn)]
ǫmicroν(0) =1radic6[ǫmicro(+)ǫν(minus) + ǫmicro(minus)ǫν(+)] +
radic
2
3ǫmicro(0)ǫν(0) (320)
ndash 12 ndash
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
F (q2) F (0) a b
V (q2) 016+002minus002 208 15
A0(q2) 025+004
minus004 157 01
A1(q2) 014+002
minus002 123 049
A2(q2) 005+002
minus002 132 149
T1(q2) 014+002
minus002 207 15
T2(q2) 014+002
minus002 122 034
T3(q2) 001+001
minus002 991 276
Table 1 B rarr Klowast
2 form factors in the light cone sum rules approach F (0) denotes the value
of form factors at q2 = 0 while a and b are the parameters in the parameterizations shown in
eq (221) [39]
quantities and are needed to be calculated using different approaches (both perturbative
and non-perturbative) like Lattice QCD QCD sum rules Light Cone sum rules etc Here
we will consider the form factors calculated in the LCSR approach [39] and their evolution
with q2 is given by
F (q2) =F (0)
1minus a(q2m2B) + b(q2m2
B)2
(221)
where the value of different parameters is given in table 1
The errors in the values of the form factors arise from number of input parameters
involved in their calculation in LCSR such as variations in the Boral parameters fluctuation
of threshold parameters errors in the b quark mass corrections from the decay constants
of involved mesons and from the Gengenbauer moments in the distribution amplitudes
It is worth mentioning here that it is possible to study this mode with the help of
QCD factorization which might discover additional sources of theoretical errors which are
overlooked in the simple form factor analysis As besides the factorizable contribution of
form factors which has been used here there are in principle non-factorizable contributions
to matrix elements as well [13] QCD factorization not only reduce the number of inde-
pendent parameters in heavy quark limit but also help us to compute the non-factorizable
corrections to B meson decays with the help of light-cone distribution amplitudes and
hard scattering kernel [53 54] The details of QCD factorization and its implications in
semileptonic and radiative B meson decays can be found in [13]
24 Numerical constraints on NP parameters
The constraints on NP parameters can be obtained from the branching ratios of B0s rarr
micro+microminus B0s rarr Xsmicro
+microminus and B0d rarr Kmicro+microminus [5 47ndash50] Due to the large hadronic uncertain-
ties the constraints obtained from the exclusive decay modes are somewhat weaker com-
pared to the inclusive ones The branching ratio of inclusive decay mode B rarr Xsmicro+microminus has
been measured by Babar [49] and Belle [50] and their measurements in low-q2 (1GeV2 le
ndash 6 ndash
JHEP02(2012)045
q2 le 6GeV2) and high-q2 (144GeV2 le q2 le 25GeV2) regions can be summarized as
B(B rarr Xsmicro+microminus)low q2 = (149plusmn 050+041
minus032)times 10minus6 (Belle)
(18plusmn 07plusmn 050)times 10minus6 (BaBar) (222)
(160plusmn 050)times 10minus6 (Average)
B(B rarr Xsmicro+microminus)high q2 = (042plusmn 012+007
minus007)times 10minus6 (Belle)
(050plusmn 025+007minus008)times 10minus6 (BaBar) (223)
(044plusmn 012)times 10minus6 (Average)
where q2 is the invariant mass squared of two muons and low-q2 region corresponds to
1GeV2 le q2 le 6GeV2 and high-q2 region corresponds to q2 ge 144GeV2
The constraints on the new V A couplings come mainly from B0d rarr Xsmicro
+microminus and B0d rarr
Kmicro+microminus [51] It has been shown in ref [51] that if RVA couplings are present only the
constraints on these couplings from above said decays came to be
10 le |RV + 36|2(47)2
+|RA minus 40|2
(48)2|RV + 28|2
(65)2+|RA minus 41|2
(66)2le 1 (224)
Similarly when we have only RprimeVA couplings the constraints on them from the same decay
will become [51]
22 le |RprimeV + 36|2 + |Rprime
A minus 40|2 le 566 |RprimeV |2 + |Rprime
A|2 le 17 (225)
These constraints are weekend when both RVA and RprimeVA couplings are present at the same
time In this case these new physics couplings are restricted to be
|RV + 28|2(65)2
+|RA minus 41|2
(66)2le 1 (226)
and
|RprimeV |2 + |Rprime
A|2 le 40 (227)
The limits on couplings corresponding to scalar-pseudoscalar (SP) operators comes
from the upper bound on B0s rarr micro+microminus which provides the limit
|RS minusRprimeS |2 + |RP minusRprime
P |2 le 044 (228)
This puts a sever constraint on the NP couplings if only RSP or RprimeSP are present However
under the condition where both types of operators are present RSP or RprimeSP these bounds
can be relaxed due to cancelation between the RSP and RprimeSP In this case B0
d rarr Xsmicro+microminus
and B0d rarr Kmicro+microminus can still bound these couplings and the stronger bound is obtained from
the measurement of later quantity which yields
|RS |2 + |RP |2 le 9 RS asymp RprimeS RS asymp Rprime
P (229)
Now the constraint on the NP tensor type couplings comes entirely from the inclusive
B0d rarr Xsmicro
+microminus decay In case when only tensor type operators are present the limits on
tensor type couplings are [51]
|CT |2 + |CTE |2 le 10 (230)
ndash 7 ndash
JHEP02(2012)045
In the present study we will examine B rarr Klowast2 (1430)micro
+microminus decays by using these NP
constraints
3 Decay rate forward-backward asymmetry and lepton polarization a-
symmetries for B rarr Klowast
2(1430)micro+microminus decay
In this section we are going to perform the calculations of some very interesting quantities
like the decay rate the forward-backward asymmetry the polarization asymmetries of
the final state lepton and the helicity fractions of the final state Klowast2 (1430) meson From
eq (27) it is straightforward to obtain the decay amplitude for B rarr Klowast2 (1430)micro
+microminus as
M(B rarr Klowast2 (1430)micro
+microminus) = minus GFα
2radic2π
VtbVlowastts
[
TmicroV lγmicrol + Tmicro
A lγmicroγ5l
+TS ll + TP lγ5l + Tmicroν
T lσmicroν l + iTmicroνE ǫmicroναβ lσαβl
]
(31)
with
TmicroV = minusF1ǫ
microναβεlowastνpKlowastαqβ + iF2εlowastmicro + iF3ε
lowast middot q(pB + pKlowast)micro + iF4εlowast middot qqmicro
TmicroA = minusF5ǫ
microναβεlowastνpKlowastαqβ + iF6εlowastmicro + iF7ε
lowast middot q(pB + pKlowast)micro + iF8εlowast middot qqmicro
TS = iF9εlowast middot q
TP = iF10εlowast middot pB
TmicroνT = CT
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
TmicroνE = CTE
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
(32)
The auxiliary functions F1 middot middot middot F13 appearing in eq (32) are defined as follows
F1 =
[
2V (q2)
mB +mKlowast
(Ceff9 +RV +Rprime
V ) +4mb
q2Ceff7 T1(q
2)
]
F2 = minus[
(mB +mKlowast)A1(q2)(Ceff
9 +RV minusRprimeV ) +
2mb
q2Ceff7 T1(q
2)(m2B minusmKlowast)
]
F3 =
[
A(q2)
mB +mKlowast
(Ceff9 +RV minusRprime
V ) +2mb
q2Ceff7
(
T1(q2) +
q2T3(q2)
m2B minusmKlowast
)]
F4 =
[
2mKlowast
q2(Ceff
9 +RV minusRprimeV )(A3(q
2)minusA0(q2))minus 2mb
q2Ceff7 T3(q
2)
]
F5 =
[
2V (q2)
mB +mKlowast
(Ceff10 +RA +Rprime
A)
]
F6 = minus[
(mB +mKlowast)A1(q2)(Ceff
10 +RA minusRprimeA)
]
F7 =
[
A(q2)
mB +mKlowast
(Ceff10 +RA minusRprime
A)
]
F8 =
[
2mKlowast
q2(Ceff
10 +RA minusRprimeA)(A3(q
2)minusA0(q2))
]
F9 =
[
minus2(RS minusRprimeS)
mKlowast
mbA0(q
2)
]
ndash 8 ndash
JHEP02(2012)045
F10 =
[
2(RP minusRprimeP )
mKlowast
mbA0(q
2)
]
F11 = minus2T1(q2)
F12 =
[
2(m2B minusm2
Klowast)
q2(T1(q
2)minus T2(q2))
]
F13 =
[
4
q2
(
T1(q2)minus T2(q
2)minus q2T3(q2)
m2B minusm2
Klowast
)]
(33)
31 Differential decay rate
The differential decay width of B rarr Klowast2 (1430)micro
+microminus in dilepton center of mass frame can
be written as
dΓ(B rarr Klowast2 (1430)micro
+microminus)
dq2=
1
(2π)31
32m3B
int u(q2)
minusu(q2)|MBrarrKlowast
2(1430)micro+microminus |2du (34)
where u = (p + pmicrominus)2 minus (p + pmicro+)2 = u(q2) cos θ and q2 = (pmicro+ + pmicrominus)2 p k pmicro+ and
pmicrominus are the four-momenta vectors of B Klowast2 (1430) micro
+ and microminus respectively and u(q2) are
given by
u(q2) =radic
m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2
radic
1minus 4m2l
q2(35)
Collecting everything together one can write the general expression of the differential decay
rate for B rarr Klowast2 (1430)micro
+microminus as
dΓ
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
18m2lm
4T q
2
3F21m
2Klowast
2q2λ+ 2F2
2m4B(λ+ 10m2
T q2) (36)
+2F23λ
2] (
2m2l + q2
)
minus[
3F25m
2Klowast
2minus 3F2
9m2B
]
K2q2λ+ 12F2
8m2l q
4λ
+2F26m
4B
[
2(
λminus 20m2T q
2)
m2l + q2
(
λ+ 10m2T q
2)]
+ 3F210m
2Bq
4λ
+2F27λ
[
2(
λminus 3q4 + 6m2T q
2)
m2Klowast
2+ q2λ
]
minus 4F2F3m4B
(
2m2l + q2
)
K1λ2
minus4F6F7m2Bλ
[
2(
K1 + 3q2)
m2l +K1q
2]
minus 24F6F8m2lm
2Bq
2λminus 12F10F6mlm3Bq
2λ
+24F7F8m2lK0q
2λ+ 12F10F7mlmBK0q2λ+ 8F11F12q
2(λ+ 10m2Tm
2B minus 10m4
T )K3
minus4F11F13(K1 + 4m2T )λq
2K3 minus 72F1F11mlm2Klowast
2q2λCT
+48F11F2mlm2Bq
2(λ+ 10m2Tm
2B minus 10m4
T )CTE minus 4F12F13K1λq2K3
+48F12F2mlm2Bq
2(
λ+ 10m2T q
2)
CTE minus 48F12F3mlq2K1CTEλ
minus24F13F2mlm2BK1λq
2CTE + 24F13F3mlq2CTEλ
2
where ml is the mass of final state muon and
λ = λ(
m2Bm
2Klowast
2 q2
)
equiv m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2 (37)
K0 = (m2B minusm2
Klowast
2) K1 =
(
m2B minusm2
Klowast
2minus q2
)
K2 = q2 minus 4m2l
K3 = q2C2T minus 4m2
l
(
C2T minus 36C2
TE
)
(38)
and the auxiliary functions are the same as defined in eq (33)
ndash 9 ndash
JHEP02(2012)045
32 Forward-backward asymmetry
Now we are in a position to explore the forward-backward asymmetry of final state leptons
in the B rarr Klowast2 (1430)micro
+microminus which is an essential observable sensitive to the new physics
effects To calculate the forward-backward asymmetry we consider the following double
differential decay rate formula for the process B rarr Klowast2 (1430)micro
+microminus
d2Γ(q2 cos θ)
dq2d cos θ=
1
(2π)31
64m3B
u(q2)|MBrarrKlowast
2(1430)micro+microminus |2 (39)
where θ is the angle between the momentum of B baryon and lminus in the dilepton rest frame
The differential and normalized FBAs for the semi-leptonic decay B rarr Klowast2 (1430)l
+lminus are
defined as
dAFB(q2)
dq2=
int 1
0d cos θ
d2Γ(q2 cos θ)
dq2d cos θminusint 0
minus1d cos θ
d2Γ(q2 cos θ)
dq2d cos θ(310)
and
AFB(q2) =
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θminusint 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θ+int 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
(311)
Following the same procedure as we did for the differential decay rate one can easily get
the expression for the forward-backward asymmetry as follows
dAFB(q2)
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
6mBm4T
[
AV AFB +ASP
FB +ATSPFB +AT
FB
]
(312a)
AV AFB = minus3(F2F5 + F1F6)q
2m2Bm
2K2
(312b)
ASPFB = 2F9mlmB
(
F3λ+ F2m2B
[
q2 minusm2B +m2
K2
])
(312c)
ATSPFB = minusq2 (F10CT + 2F9CTE)mB
(
2F12
(
m2B minusm2
K2minus q2
)
(312d)
minusF13λ+ 2F11
(
m2B + 3m2
K2minus q2
))
ATFB = minus2ml
(
12F12F5q2CTEm
2K2
+ 12F11F5CTEm2K2
(
m2B minusm2
K2
)
(312e)
+F13λCT
(
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F12CT
(
m2B minusm2
K2minus q2
) (
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F11CT
(
F6m2B
(
m2B + 9m2
K2minus q2
)
minus(
m2B + 3m2
K2minus q2
) (
F8q2 + F7
(
m2B minusm2
K2
)))
and the expression of the differential decay rate is given in eq (36)
33 Lepton polarization asymmetries
In the rest frame of the lepton microminus the unit vectors along longitudinal normal and transver-
sal component of the microminus can be defined as [55]
sminusmicroL = (0 ~eL) =
(
0~pminus|~pminus|
)
sminusmicroN = (0 ~eN ) =
0~k times ~pminus∣
∣
∣
~k times ~pminus∣
∣
∣
(313)
sminusmicroT = (0 ~eT ) = (0 ~eN times ~eL)
ndash 10 ndash
JHEP02(2012)045
where ~pminus and ~k are the three-momenta of the microminus and Klowast2 (1430) meson respectively in the
center mass (CM) frame of micro+microminus system Lorentz transformation is used to boost the
longitudinal component of the lepton polarization to the CM frame of the lepton pair as
(
sminusmicroL
)
CM=
( |~pminus|ml
El~pminusml |~pminus|
)
(314)
where El and ml are the energy and mass of the final state muon The normal and
transverse components remain unchanged under the Lorentz boost The longitudinal (PL)
normal (PN ) and transverse (PT ) polarizations of lepton can be defined as
P(∓)i (q2) =
dΓdq2
(~ξ∓ = ~e∓)minus dΓdq2
(~ξ∓ = minus~e∓)dΓdq2
(~ξ∓ = ~e∓) + dΓdq2
(~ξ∓ = minus~e∓)(315)
where i = L N T and ~ξ∓ is the spin direction along the leptons micro∓ The differential
decay rate for polarized lepton l∓ in B rarr Klowast2 (1430)micro
+microminus decay along any spin direction~ξ∓ is related to the unpolarized decay rate (36) with the following relation
dΓ(~ξ∓)
dq2=
1
2
(
dΓ
dq2
)
[1 + (P∓L ~e∓L + P∓
N~e∓N + P∓T ~e∓T ) middot ~ξ∓] (316)
We can achieve the expressions of longitudinal normal and transverse polarizations for
B rarr Klowast2 (1430)micro
+microminus decays as collected below The longitudinal lepton polarization can
be written as
PL prop1
36m2Bm
4T
4u(q2)radicλ[
P V AL + PSP
L + P TL
]
(317a)
P V AL = ml
(
2λF2 (F6 minusF7)m4B +
(
3λF1F5q2 + 2F2m
2B
(
10q2F6m2B + λF7
))
m2Klowast
2
+2λF3
(
F6
(
q2 minusm2B +m2
Klowast
2
)
m2B + λF7
))
(317b)
PSPL = 3mlλF9mB
(
minus2mlF8q2 minusF10mBq
2 + 2ml
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
(317c)
P TL = m2
lF11
(
24 (CTEF1 minus CTF5)m2Klowast
2λ+ 4CTλF3
(
m2B + 3m2
Klowast
2minus q2
)
+4m2B (4CTEF6 minus CTF2)
(
10(
m2B minusm2
Klowast
2
)
m2Klowast
2+ λ
))
+m2lF12
(
4m2B (4CTEF6 minus CTF2)
(
10q2m2Klowast
2+ λ
)
minus 4CTF3
(
q2 minusm2B +m2
Klowast
2
))
+m2lF13
(
2CTλminus 4CTF2m2B
(
m2B minusm2
Klowast
2minus q2
)
minus 2CTλ2F3
)
(317d)
ndash 11 ndash
JHEP02(2012)045
Similarly the normal lepton polarization is
PN prop minusπu(q2)t
(12m2Bm
4T
(λ
t)32
[
P V AN + PSP
N + P TN
]
(318a)
P V AN = 2ml
(
F2
(
F8q4 minus
(
(F6 minusF7 + F8)m2B + (minus3F1 + F7 minusF8)m
2Klowast
2
)
q2 (318b)
+(
m2B minusm2
Klowast
2
)
m2B
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
+ λF3
(
F8q2 minusF6m
2B + F7
(
m2B minusm2
Klowast
2
)))
PSPN = mBλ
(
F3F10q2 +
(
q2 minus 4m2l
)
F7F9
)
(318c)
minus(
F2F10q2 +
(
q2 minus 4m2l
)
F6F9
)
m3B
(
m2B minusm2
Klowast
2minus q2
)
P TN = F13
(
8m2l λCTE
(
F8q2 minusF6m
2B minusF7
(
m2Klowast
2minusm2
B
))
+ 4mlmBλCTEF10q2)
+F12
(
16m2lCTE
(
F6m2BminusF7
(
m2Bminusm2
Klowast
2
)
minusF8q2minusmB
2mlF10q
2
)
(
m2Bminusm2
Klowast
2minusq2
)
+ 6(
4m2l + q2
)
CTEF1q2m2
Klowast
2+ 3
(
q2 minus 4m2)
CTF5q2m2
Klowast
2
)
+F11
(
minus16m2lCTE
(
F8q2 + F7
(
m2B minusm2
Klowast
2
)
+mB
2mlF10q
2
)
(
m2B + 3m2
Klowast
2minus q2
)
+6m2Klowast
2
(
4m2l + q2
)
(
CTEF1
(
m2B minusm2
Klowast
2
)
minus CTF2m2B
)
+3(
4m2l minus q2
)
CTF5m2Klowast
2
(
m2Klowast
2minusm2
B
)
+4CTEF6m2B
(
4m2l
(
m2B + 6m2
Klowast
2minus q2
)
minus 3q2m2Klowast
2
)
)
(318d)
and the transverse one is given by
PT propiπλq2u(q2)
12mBm2Klowast
2
λCTEF13
(
4F2m2B minus 3F5m
2Klowast
2+ F3
(
q2 minus 5m2B +m2
Klowast
2
))
(319)
minus2F12
(
2CTE
((
8F3m2B minus (2F3 + 3F5)m
2Klowast
2
)
q2 + 4F2m2B
(
2m2B +m2
Klowast
2minus 2q2
)
minus(
m2Bminusm2
Klowast
2
)(
8F3m2B + (4F3 + 3F5)m
2Klowast
2
))
minus3CTF1m2Klowast
2
(
q2minus3m2B + 3m2
Klowast
2
))
+2F11
(
2CTE
(
3F5m2Klowast
2
(
3m2B +m2
Klowast
2minus q2
)
minus 4F2
(
2m2B + 3m2
Klowast
2minus 2q2
)
m2B
+2F3
(
7m2Klowast
2q2minus4q4+6λ+4m2
B
(
q2+5m2Klowast
2
)))
minus3CTF1m2Klowast
2
(
3m2B+m2
Klowast
2minusq2
)
34 Helicity fractions
Helicity fraction is an observable associated with polarization of the out going meson that
is almost free of hadronic uncertainties The spin-2 polarization tensor which satisfies
ǫmicroνkν = 0 with k being the momentum is symmetric and traceless It can be constructed
by the vector polarization ǫmicro as
ǫmicroν(plusmn2) = ǫmicro(plusmn)ǫν(plusmn) ǫmicroν(plusmn1) =1radic2[ǫmicro(plusmn)ǫν(0) + ǫmicro(0)ǫν(plusmn)]
ǫmicroν(0) =1radic6[ǫmicro(+)ǫν(minus) + ǫmicro(minus)ǫν(+)] +
radic
2
3ǫmicro(0)ǫν(0) (320)
ndash 12 ndash
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
q2 le 6GeV2) and high-q2 (144GeV2 le q2 le 25GeV2) regions can be summarized as
B(B rarr Xsmicro+microminus)low q2 = (149plusmn 050+041
minus032)times 10minus6 (Belle)
(18plusmn 07plusmn 050)times 10minus6 (BaBar) (222)
(160plusmn 050)times 10minus6 (Average)
B(B rarr Xsmicro+microminus)high q2 = (042plusmn 012+007
minus007)times 10minus6 (Belle)
(050plusmn 025+007minus008)times 10minus6 (BaBar) (223)
(044plusmn 012)times 10minus6 (Average)
where q2 is the invariant mass squared of two muons and low-q2 region corresponds to
1GeV2 le q2 le 6GeV2 and high-q2 region corresponds to q2 ge 144GeV2
The constraints on the new V A couplings come mainly from B0d rarr Xsmicro
+microminus and B0d rarr
Kmicro+microminus [51] It has been shown in ref [51] that if RVA couplings are present only the
constraints on these couplings from above said decays came to be
10 le |RV + 36|2(47)2
+|RA minus 40|2
(48)2|RV + 28|2
(65)2+|RA minus 41|2
(66)2le 1 (224)
Similarly when we have only RprimeVA couplings the constraints on them from the same decay
will become [51]
22 le |RprimeV + 36|2 + |Rprime
A minus 40|2 le 566 |RprimeV |2 + |Rprime
A|2 le 17 (225)
These constraints are weekend when both RVA and RprimeVA couplings are present at the same
time In this case these new physics couplings are restricted to be
|RV + 28|2(65)2
+|RA minus 41|2
(66)2le 1 (226)
and
|RprimeV |2 + |Rprime
A|2 le 40 (227)
The limits on couplings corresponding to scalar-pseudoscalar (SP) operators comes
from the upper bound on B0s rarr micro+microminus which provides the limit
|RS minusRprimeS |2 + |RP minusRprime
P |2 le 044 (228)
This puts a sever constraint on the NP couplings if only RSP or RprimeSP are present However
under the condition where both types of operators are present RSP or RprimeSP these bounds
can be relaxed due to cancelation between the RSP and RprimeSP In this case B0
d rarr Xsmicro+microminus
and B0d rarr Kmicro+microminus can still bound these couplings and the stronger bound is obtained from
the measurement of later quantity which yields
|RS |2 + |RP |2 le 9 RS asymp RprimeS RS asymp Rprime
P (229)
Now the constraint on the NP tensor type couplings comes entirely from the inclusive
B0d rarr Xsmicro
+microminus decay In case when only tensor type operators are present the limits on
tensor type couplings are [51]
|CT |2 + |CTE |2 le 10 (230)
ndash 7 ndash
JHEP02(2012)045
In the present study we will examine B rarr Klowast2 (1430)micro
+microminus decays by using these NP
constraints
3 Decay rate forward-backward asymmetry and lepton polarization a-
symmetries for B rarr Klowast
2(1430)micro+microminus decay
In this section we are going to perform the calculations of some very interesting quantities
like the decay rate the forward-backward asymmetry the polarization asymmetries of
the final state lepton and the helicity fractions of the final state Klowast2 (1430) meson From
eq (27) it is straightforward to obtain the decay amplitude for B rarr Klowast2 (1430)micro
+microminus as
M(B rarr Klowast2 (1430)micro
+microminus) = minus GFα
2radic2π
VtbVlowastts
[
TmicroV lγmicrol + Tmicro
A lγmicroγ5l
+TS ll + TP lγ5l + Tmicroν
T lσmicroν l + iTmicroνE ǫmicroναβ lσαβl
]
(31)
with
TmicroV = minusF1ǫ
microναβεlowastνpKlowastαqβ + iF2εlowastmicro + iF3ε
lowast middot q(pB + pKlowast)micro + iF4εlowast middot qqmicro
TmicroA = minusF5ǫ
microναβεlowastνpKlowastαqβ + iF6εlowastmicro + iF7ε
lowast middot q(pB + pKlowast)micro + iF8εlowast middot qqmicro
TS = iF9εlowast middot q
TP = iF10εlowast middot pB
TmicroνT = CT
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
TmicroνE = CTE
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
(32)
The auxiliary functions F1 middot middot middot F13 appearing in eq (32) are defined as follows
F1 =
[
2V (q2)
mB +mKlowast
(Ceff9 +RV +Rprime
V ) +4mb
q2Ceff7 T1(q
2)
]
F2 = minus[
(mB +mKlowast)A1(q2)(Ceff
9 +RV minusRprimeV ) +
2mb
q2Ceff7 T1(q
2)(m2B minusmKlowast)
]
F3 =
[
A(q2)
mB +mKlowast
(Ceff9 +RV minusRprime
V ) +2mb
q2Ceff7
(
T1(q2) +
q2T3(q2)
m2B minusmKlowast
)]
F4 =
[
2mKlowast
q2(Ceff
9 +RV minusRprimeV )(A3(q
2)minusA0(q2))minus 2mb
q2Ceff7 T3(q
2)
]
F5 =
[
2V (q2)
mB +mKlowast
(Ceff10 +RA +Rprime
A)
]
F6 = minus[
(mB +mKlowast)A1(q2)(Ceff
10 +RA minusRprimeA)
]
F7 =
[
A(q2)
mB +mKlowast
(Ceff10 +RA minusRprime
A)
]
F8 =
[
2mKlowast
q2(Ceff
10 +RA minusRprimeA)(A3(q
2)minusA0(q2))
]
F9 =
[
minus2(RS minusRprimeS)
mKlowast
mbA0(q
2)
]
ndash 8 ndash
JHEP02(2012)045
F10 =
[
2(RP minusRprimeP )
mKlowast
mbA0(q
2)
]
F11 = minus2T1(q2)
F12 =
[
2(m2B minusm2
Klowast)
q2(T1(q
2)minus T2(q2))
]
F13 =
[
4
q2
(
T1(q2)minus T2(q
2)minus q2T3(q2)
m2B minusm2
Klowast
)]
(33)
31 Differential decay rate
The differential decay width of B rarr Klowast2 (1430)micro
+microminus in dilepton center of mass frame can
be written as
dΓ(B rarr Klowast2 (1430)micro
+microminus)
dq2=
1
(2π)31
32m3B
int u(q2)
minusu(q2)|MBrarrKlowast
2(1430)micro+microminus |2du (34)
where u = (p + pmicrominus)2 minus (p + pmicro+)2 = u(q2) cos θ and q2 = (pmicro+ + pmicrominus)2 p k pmicro+ and
pmicrominus are the four-momenta vectors of B Klowast2 (1430) micro
+ and microminus respectively and u(q2) are
given by
u(q2) =radic
m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2
radic
1minus 4m2l
q2(35)
Collecting everything together one can write the general expression of the differential decay
rate for B rarr Klowast2 (1430)micro
+microminus as
dΓ
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
18m2lm
4T q
2
3F21m
2Klowast
2q2λ+ 2F2
2m4B(λ+ 10m2
T q2) (36)
+2F23λ
2] (
2m2l + q2
)
minus[
3F25m
2Klowast
2minus 3F2
9m2B
]
K2q2λ+ 12F2
8m2l q
4λ
+2F26m
4B
[
2(
λminus 20m2T q
2)
m2l + q2
(
λ+ 10m2T q
2)]
+ 3F210m
2Bq
4λ
+2F27λ
[
2(
λminus 3q4 + 6m2T q
2)
m2Klowast
2+ q2λ
]
minus 4F2F3m4B
(
2m2l + q2
)
K1λ2
minus4F6F7m2Bλ
[
2(
K1 + 3q2)
m2l +K1q
2]
minus 24F6F8m2lm
2Bq
2λminus 12F10F6mlm3Bq
2λ
+24F7F8m2lK0q
2λ+ 12F10F7mlmBK0q2λ+ 8F11F12q
2(λ+ 10m2Tm
2B minus 10m4
T )K3
minus4F11F13(K1 + 4m2T )λq
2K3 minus 72F1F11mlm2Klowast
2q2λCT
+48F11F2mlm2Bq
2(λ+ 10m2Tm
2B minus 10m4
T )CTE minus 4F12F13K1λq2K3
+48F12F2mlm2Bq
2(
λ+ 10m2T q
2)
CTE minus 48F12F3mlq2K1CTEλ
minus24F13F2mlm2BK1λq
2CTE + 24F13F3mlq2CTEλ
2
where ml is the mass of final state muon and
λ = λ(
m2Bm
2Klowast
2 q2
)
equiv m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2 (37)
K0 = (m2B minusm2
Klowast
2) K1 =
(
m2B minusm2
Klowast
2minus q2
)
K2 = q2 minus 4m2l
K3 = q2C2T minus 4m2
l
(
C2T minus 36C2
TE
)
(38)
and the auxiliary functions are the same as defined in eq (33)
ndash 9 ndash
JHEP02(2012)045
32 Forward-backward asymmetry
Now we are in a position to explore the forward-backward asymmetry of final state leptons
in the B rarr Klowast2 (1430)micro
+microminus which is an essential observable sensitive to the new physics
effects To calculate the forward-backward asymmetry we consider the following double
differential decay rate formula for the process B rarr Klowast2 (1430)micro
+microminus
d2Γ(q2 cos θ)
dq2d cos θ=
1
(2π)31
64m3B
u(q2)|MBrarrKlowast
2(1430)micro+microminus |2 (39)
where θ is the angle between the momentum of B baryon and lminus in the dilepton rest frame
The differential and normalized FBAs for the semi-leptonic decay B rarr Klowast2 (1430)l
+lminus are
defined as
dAFB(q2)
dq2=
int 1
0d cos θ
d2Γ(q2 cos θ)
dq2d cos θminusint 0
minus1d cos θ
d2Γ(q2 cos θ)
dq2d cos θ(310)
and
AFB(q2) =
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θminusint 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θ+int 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
(311)
Following the same procedure as we did for the differential decay rate one can easily get
the expression for the forward-backward asymmetry as follows
dAFB(q2)
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
6mBm4T
[
AV AFB +ASP
FB +ATSPFB +AT
FB
]
(312a)
AV AFB = minus3(F2F5 + F1F6)q
2m2Bm
2K2
(312b)
ASPFB = 2F9mlmB
(
F3λ+ F2m2B
[
q2 minusm2B +m2
K2
])
(312c)
ATSPFB = minusq2 (F10CT + 2F9CTE)mB
(
2F12
(
m2B minusm2
K2minus q2
)
(312d)
minusF13λ+ 2F11
(
m2B + 3m2
K2minus q2
))
ATFB = minus2ml
(
12F12F5q2CTEm
2K2
+ 12F11F5CTEm2K2
(
m2B minusm2
K2
)
(312e)
+F13λCT
(
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F12CT
(
m2B minusm2
K2minus q2
) (
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F11CT
(
F6m2B
(
m2B + 9m2
K2minus q2
)
minus(
m2B + 3m2
K2minus q2
) (
F8q2 + F7
(
m2B minusm2
K2
)))
and the expression of the differential decay rate is given in eq (36)
33 Lepton polarization asymmetries
In the rest frame of the lepton microminus the unit vectors along longitudinal normal and transver-
sal component of the microminus can be defined as [55]
sminusmicroL = (0 ~eL) =
(
0~pminus|~pminus|
)
sminusmicroN = (0 ~eN ) =
0~k times ~pminus∣
∣
∣
~k times ~pminus∣
∣
∣
(313)
sminusmicroT = (0 ~eT ) = (0 ~eN times ~eL)
ndash 10 ndash
JHEP02(2012)045
where ~pminus and ~k are the three-momenta of the microminus and Klowast2 (1430) meson respectively in the
center mass (CM) frame of micro+microminus system Lorentz transformation is used to boost the
longitudinal component of the lepton polarization to the CM frame of the lepton pair as
(
sminusmicroL
)
CM=
( |~pminus|ml
El~pminusml |~pminus|
)
(314)
where El and ml are the energy and mass of the final state muon The normal and
transverse components remain unchanged under the Lorentz boost The longitudinal (PL)
normal (PN ) and transverse (PT ) polarizations of lepton can be defined as
P(∓)i (q2) =
dΓdq2
(~ξ∓ = ~e∓)minus dΓdq2
(~ξ∓ = minus~e∓)dΓdq2
(~ξ∓ = ~e∓) + dΓdq2
(~ξ∓ = minus~e∓)(315)
where i = L N T and ~ξ∓ is the spin direction along the leptons micro∓ The differential
decay rate for polarized lepton l∓ in B rarr Klowast2 (1430)micro
+microminus decay along any spin direction~ξ∓ is related to the unpolarized decay rate (36) with the following relation
dΓ(~ξ∓)
dq2=
1
2
(
dΓ
dq2
)
[1 + (P∓L ~e∓L + P∓
N~e∓N + P∓T ~e∓T ) middot ~ξ∓] (316)
We can achieve the expressions of longitudinal normal and transverse polarizations for
B rarr Klowast2 (1430)micro
+microminus decays as collected below The longitudinal lepton polarization can
be written as
PL prop1
36m2Bm
4T
4u(q2)radicλ[
P V AL + PSP
L + P TL
]
(317a)
P V AL = ml
(
2λF2 (F6 minusF7)m4B +
(
3λF1F5q2 + 2F2m
2B
(
10q2F6m2B + λF7
))
m2Klowast
2
+2λF3
(
F6
(
q2 minusm2B +m2
Klowast
2
)
m2B + λF7
))
(317b)
PSPL = 3mlλF9mB
(
minus2mlF8q2 minusF10mBq
2 + 2ml
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
(317c)
P TL = m2
lF11
(
24 (CTEF1 minus CTF5)m2Klowast
2λ+ 4CTλF3
(
m2B + 3m2
Klowast
2minus q2
)
+4m2B (4CTEF6 minus CTF2)
(
10(
m2B minusm2
Klowast
2
)
m2Klowast
2+ λ
))
+m2lF12
(
4m2B (4CTEF6 minus CTF2)
(
10q2m2Klowast
2+ λ
)
minus 4CTF3
(
q2 minusm2B +m2
Klowast
2
))
+m2lF13
(
2CTλminus 4CTF2m2B
(
m2B minusm2
Klowast
2minus q2
)
minus 2CTλ2F3
)
(317d)
ndash 11 ndash
JHEP02(2012)045
Similarly the normal lepton polarization is
PN prop minusπu(q2)t
(12m2Bm
4T
(λ
t)32
[
P V AN + PSP
N + P TN
]
(318a)
P V AN = 2ml
(
F2
(
F8q4 minus
(
(F6 minusF7 + F8)m2B + (minus3F1 + F7 minusF8)m
2Klowast
2
)
q2 (318b)
+(
m2B minusm2
Klowast
2
)
m2B
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
+ λF3
(
F8q2 minusF6m
2B + F7
(
m2B minusm2
Klowast
2
)))
PSPN = mBλ
(
F3F10q2 +
(
q2 minus 4m2l
)
F7F9
)
(318c)
minus(
F2F10q2 +
(
q2 minus 4m2l
)
F6F9
)
m3B
(
m2B minusm2
Klowast
2minus q2
)
P TN = F13
(
8m2l λCTE
(
F8q2 minusF6m
2B minusF7
(
m2Klowast
2minusm2
B
))
+ 4mlmBλCTEF10q2)
+F12
(
16m2lCTE
(
F6m2BminusF7
(
m2Bminusm2
Klowast
2
)
minusF8q2minusmB
2mlF10q
2
)
(
m2Bminusm2
Klowast
2minusq2
)
+ 6(
4m2l + q2
)
CTEF1q2m2
Klowast
2+ 3
(
q2 minus 4m2)
CTF5q2m2
Klowast
2
)
+F11
(
minus16m2lCTE
(
F8q2 + F7
(
m2B minusm2
Klowast
2
)
+mB
2mlF10q
2
)
(
m2B + 3m2
Klowast
2minus q2
)
+6m2Klowast
2
(
4m2l + q2
)
(
CTEF1
(
m2B minusm2
Klowast
2
)
minus CTF2m2B
)
+3(
4m2l minus q2
)
CTF5m2Klowast
2
(
m2Klowast
2minusm2
B
)
+4CTEF6m2B
(
4m2l
(
m2B + 6m2
Klowast
2minus q2
)
minus 3q2m2Klowast
2
)
)
(318d)
and the transverse one is given by
PT propiπλq2u(q2)
12mBm2Klowast
2
λCTEF13
(
4F2m2B minus 3F5m
2Klowast
2+ F3
(
q2 minus 5m2B +m2
Klowast
2
))
(319)
minus2F12
(
2CTE
((
8F3m2B minus (2F3 + 3F5)m
2Klowast
2
)
q2 + 4F2m2B
(
2m2B +m2
Klowast
2minus 2q2
)
minus(
m2Bminusm2
Klowast
2
)(
8F3m2B + (4F3 + 3F5)m
2Klowast
2
))
minus3CTF1m2Klowast
2
(
q2minus3m2B + 3m2
Klowast
2
))
+2F11
(
2CTE
(
3F5m2Klowast
2
(
3m2B +m2
Klowast
2minus q2
)
minus 4F2
(
2m2B + 3m2
Klowast
2minus 2q2
)
m2B
+2F3
(
7m2Klowast
2q2minus4q4+6λ+4m2
B
(
q2+5m2Klowast
2
)))
minus3CTF1m2Klowast
2
(
3m2B+m2
Klowast
2minusq2
)
34 Helicity fractions
Helicity fraction is an observable associated with polarization of the out going meson that
is almost free of hadronic uncertainties The spin-2 polarization tensor which satisfies
ǫmicroνkν = 0 with k being the momentum is symmetric and traceless It can be constructed
by the vector polarization ǫmicro as
ǫmicroν(plusmn2) = ǫmicro(plusmn)ǫν(plusmn) ǫmicroν(plusmn1) =1radic2[ǫmicro(plusmn)ǫν(0) + ǫmicro(0)ǫν(plusmn)]
ǫmicroν(0) =1radic6[ǫmicro(+)ǫν(minus) + ǫmicro(minus)ǫν(+)] +
radic
2
3ǫmicro(0)ǫν(0) (320)
ndash 12 ndash
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
In the present study we will examine B rarr Klowast2 (1430)micro
+microminus decays by using these NP
constraints
3 Decay rate forward-backward asymmetry and lepton polarization a-
symmetries for B rarr Klowast
2(1430)micro+microminus decay
In this section we are going to perform the calculations of some very interesting quantities
like the decay rate the forward-backward asymmetry the polarization asymmetries of
the final state lepton and the helicity fractions of the final state Klowast2 (1430) meson From
eq (27) it is straightforward to obtain the decay amplitude for B rarr Klowast2 (1430)micro
+microminus as
M(B rarr Klowast2 (1430)micro
+microminus) = minus GFα
2radic2π
VtbVlowastts
[
TmicroV lγmicrol + Tmicro
A lγmicroγ5l
+TS ll + TP lγ5l + Tmicroν
T lσmicroν l + iTmicroνE ǫmicroναβ lσαβl
]
(31)
with
TmicroV = minusF1ǫ
microναβεlowastνpKlowastαqβ + iF2εlowastmicro + iF3ε
lowast middot q(pB + pKlowast)micro + iF4εlowast middot qqmicro
TmicroA = minusF5ǫ
microναβεlowastνpKlowastαqβ + iF6εlowastmicro + iF7ε
lowast middot q(pB + pKlowast)micro + iF8εlowast middot qqmicro
TS = iF9εlowast middot q
TP = iF10εlowast middot pB
TmicroνT = CT
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
TmicroνE = CTE
(
iF11ǫmicroναβεlowastα(pB + pKlowast)β + iF12ǫ
microναβεlowastαqβ minus iF13ǫmicroναβεlowast middot qpαKlowastqβ
)
(32)
The auxiliary functions F1 middot middot middot F13 appearing in eq (32) are defined as follows
F1 =
[
2V (q2)
mB +mKlowast
(Ceff9 +RV +Rprime
V ) +4mb
q2Ceff7 T1(q
2)
]
F2 = minus[
(mB +mKlowast)A1(q2)(Ceff
9 +RV minusRprimeV ) +
2mb
q2Ceff7 T1(q
2)(m2B minusmKlowast)
]
F3 =
[
A(q2)
mB +mKlowast
(Ceff9 +RV minusRprime
V ) +2mb
q2Ceff7
(
T1(q2) +
q2T3(q2)
m2B minusmKlowast
)]
F4 =
[
2mKlowast
q2(Ceff
9 +RV minusRprimeV )(A3(q
2)minusA0(q2))minus 2mb
q2Ceff7 T3(q
2)
]
F5 =
[
2V (q2)
mB +mKlowast
(Ceff10 +RA +Rprime
A)
]
F6 = minus[
(mB +mKlowast)A1(q2)(Ceff
10 +RA minusRprimeA)
]
F7 =
[
A(q2)
mB +mKlowast
(Ceff10 +RA minusRprime
A)
]
F8 =
[
2mKlowast
q2(Ceff
10 +RA minusRprimeA)(A3(q
2)minusA0(q2))
]
F9 =
[
minus2(RS minusRprimeS)
mKlowast
mbA0(q
2)
]
ndash 8 ndash
JHEP02(2012)045
F10 =
[
2(RP minusRprimeP )
mKlowast
mbA0(q
2)
]
F11 = minus2T1(q2)
F12 =
[
2(m2B minusm2
Klowast)
q2(T1(q
2)minus T2(q2))
]
F13 =
[
4
q2
(
T1(q2)minus T2(q
2)minus q2T3(q2)
m2B minusm2
Klowast
)]
(33)
31 Differential decay rate
The differential decay width of B rarr Klowast2 (1430)micro
+microminus in dilepton center of mass frame can
be written as
dΓ(B rarr Klowast2 (1430)micro
+microminus)
dq2=
1
(2π)31
32m3B
int u(q2)
minusu(q2)|MBrarrKlowast
2(1430)micro+microminus |2du (34)
where u = (p + pmicrominus)2 minus (p + pmicro+)2 = u(q2) cos θ and q2 = (pmicro+ + pmicrominus)2 p k pmicro+ and
pmicrominus are the four-momenta vectors of B Klowast2 (1430) micro
+ and microminus respectively and u(q2) are
given by
u(q2) =radic
m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2
radic
1minus 4m2l
q2(35)
Collecting everything together one can write the general expression of the differential decay
rate for B rarr Klowast2 (1430)micro
+microminus as
dΓ
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
18m2lm
4T q
2
3F21m
2Klowast
2q2λ+ 2F2
2m4B(λ+ 10m2
T q2) (36)
+2F23λ
2] (
2m2l + q2
)
minus[
3F25m
2Klowast
2minus 3F2
9m2B
]
K2q2λ+ 12F2
8m2l q
4λ
+2F26m
4B
[
2(
λminus 20m2T q
2)
m2l + q2
(
λ+ 10m2T q
2)]
+ 3F210m
2Bq
4λ
+2F27λ
[
2(
λminus 3q4 + 6m2T q
2)
m2Klowast
2+ q2λ
]
minus 4F2F3m4B
(
2m2l + q2
)
K1λ2
minus4F6F7m2Bλ
[
2(
K1 + 3q2)
m2l +K1q
2]
minus 24F6F8m2lm
2Bq
2λminus 12F10F6mlm3Bq
2λ
+24F7F8m2lK0q
2λ+ 12F10F7mlmBK0q2λ+ 8F11F12q
2(λ+ 10m2Tm
2B minus 10m4
T )K3
minus4F11F13(K1 + 4m2T )λq
2K3 minus 72F1F11mlm2Klowast
2q2λCT
+48F11F2mlm2Bq
2(λ+ 10m2Tm
2B minus 10m4
T )CTE minus 4F12F13K1λq2K3
+48F12F2mlm2Bq
2(
λ+ 10m2T q
2)
CTE minus 48F12F3mlq2K1CTEλ
minus24F13F2mlm2BK1λq
2CTE + 24F13F3mlq2CTEλ
2
where ml is the mass of final state muon and
λ = λ(
m2Bm
2Klowast
2 q2
)
equiv m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2 (37)
K0 = (m2B minusm2
Klowast
2) K1 =
(
m2B minusm2
Klowast
2minus q2
)
K2 = q2 minus 4m2l
K3 = q2C2T minus 4m2
l
(
C2T minus 36C2
TE
)
(38)
and the auxiliary functions are the same as defined in eq (33)
ndash 9 ndash
JHEP02(2012)045
32 Forward-backward asymmetry
Now we are in a position to explore the forward-backward asymmetry of final state leptons
in the B rarr Klowast2 (1430)micro
+microminus which is an essential observable sensitive to the new physics
effects To calculate the forward-backward asymmetry we consider the following double
differential decay rate formula for the process B rarr Klowast2 (1430)micro
+microminus
d2Γ(q2 cos θ)
dq2d cos θ=
1
(2π)31
64m3B
u(q2)|MBrarrKlowast
2(1430)micro+microminus |2 (39)
where θ is the angle between the momentum of B baryon and lminus in the dilepton rest frame
The differential and normalized FBAs for the semi-leptonic decay B rarr Klowast2 (1430)l
+lminus are
defined as
dAFB(q2)
dq2=
int 1
0d cos θ
d2Γ(q2 cos θ)
dq2d cos θminusint 0
minus1d cos θ
d2Γ(q2 cos θ)
dq2d cos θ(310)
and
AFB(q2) =
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θminusint 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θ+int 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
(311)
Following the same procedure as we did for the differential decay rate one can easily get
the expression for the forward-backward asymmetry as follows
dAFB(q2)
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
6mBm4T
[
AV AFB +ASP
FB +ATSPFB +AT
FB
]
(312a)
AV AFB = minus3(F2F5 + F1F6)q
2m2Bm
2K2
(312b)
ASPFB = 2F9mlmB
(
F3λ+ F2m2B
[
q2 minusm2B +m2
K2
])
(312c)
ATSPFB = minusq2 (F10CT + 2F9CTE)mB
(
2F12
(
m2B minusm2
K2minus q2
)
(312d)
minusF13λ+ 2F11
(
m2B + 3m2
K2minus q2
))
ATFB = minus2ml
(
12F12F5q2CTEm
2K2
+ 12F11F5CTEm2K2
(
m2B minusm2
K2
)
(312e)
+F13λCT
(
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F12CT
(
m2B minusm2
K2minus q2
) (
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F11CT
(
F6m2B
(
m2B + 9m2
K2minus q2
)
minus(
m2B + 3m2
K2minus q2
) (
F8q2 + F7
(
m2B minusm2
K2
)))
and the expression of the differential decay rate is given in eq (36)
33 Lepton polarization asymmetries
In the rest frame of the lepton microminus the unit vectors along longitudinal normal and transver-
sal component of the microminus can be defined as [55]
sminusmicroL = (0 ~eL) =
(
0~pminus|~pminus|
)
sminusmicroN = (0 ~eN ) =
0~k times ~pminus∣
∣
∣
~k times ~pminus∣
∣
∣
(313)
sminusmicroT = (0 ~eT ) = (0 ~eN times ~eL)
ndash 10 ndash
JHEP02(2012)045
where ~pminus and ~k are the three-momenta of the microminus and Klowast2 (1430) meson respectively in the
center mass (CM) frame of micro+microminus system Lorentz transformation is used to boost the
longitudinal component of the lepton polarization to the CM frame of the lepton pair as
(
sminusmicroL
)
CM=
( |~pminus|ml
El~pminusml |~pminus|
)
(314)
where El and ml are the energy and mass of the final state muon The normal and
transverse components remain unchanged under the Lorentz boost The longitudinal (PL)
normal (PN ) and transverse (PT ) polarizations of lepton can be defined as
P(∓)i (q2) =
dΓdq2
(~ξ∓ = ~e∓)minus dΓdq2
(~ξ∓ = minus~e∓)dΓdq2
(~ξ∓ = ~e∓) + dΓdq2
(~ξ∓ = minus~e∓)(315)
where i = L N T and ~ξ∓ is the spin direction along the leptons micro∓ The differential
decay rate for polarized lepton l∓ in B rarr Klowast2 (1430)micro
+microminus decay along any spin direction~ξ∓ is related to the unpolarized decay rate (36) with the following relation
dΓ(~ξ∓)
dq2=
1
2
(
dΓ
dq2
)
[1 + (P∓L ~e∓L + P∓
N~e∓N + P∓T ~e∓T ) middot ~ξ∓] (316)
We can achieve the expressions of longitudinal normal and transverse polarizations for
B rarr Klowast2 (1430)micro
+microminus decays as collected below The longitudinal lepton polarization can
be written as
PL prop1
36m2Bm
4T
4u(q2)radicλ[
P V AL + PSP
L + P TL
]
(317a)
P V AL = ml
(
2λF2 (F6 minusF7)m4B +
(
3λF1F5q2 + 2F2m
2B
(
10q2F6m2B + λF7
))
m2Klowast
2
+2λF3
(
F6
(
q2 minusm2B +m2
Klowast
2
)
m2B + λF7
))
(317b)
PSPL = 3mlλF9mB
(
minus2mlF8q2 minusF10mBq
2 + 2ml
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
(317c)
P TL = m2
lF11
(
24 (CTEF1 minus CTF5)m2Klowast
2λ+ 4CTλF3
(
m2B + 3m2
Klowast
2minus q2
)
+4m2B (4CTEF6 minus CTF2)
(
10(
m2B minusm2
Klowast
2
)
m2Klowast
2+ λ
))
+m2lF12
(
4m2B (4CTEF6 minus CTF2)
(
10q2m2Klowast
2+ λ
)
minus 4CTF3
(
q2 minusm2B +m2
Klowast
2
))
+m2lF13
(
2CTλminus 4CTF2m2B
(
m2B minusm2
Klowast
2minus q2
)
minus 2CTλ2F3
)
(317d)
ndash 11 ndash
JHEP02(2012)045
Similarly the normal lepton polarization is
PN prop minusπu(q2)t
(12m2Bm
4T
(λ
t)32
[
P V AN + PSP
N + P TN
]
(318a)
P V AN = 2ml
(
F2
(
F8q4 minus
(
(F6 minusF7 + F8)m2B + (minus3F1 + F7 minusF8)m
2Klowast
2
)
q2 (318b)
+(
m2B minusm2
Klowast
2
)
m2B
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
+ λF3
(
F8q2 minusF6m
2B + F7
(
m2B minusm2
Klowast
2
)))
PSPN = mBλ
(
F3F10q2 +
(
q2 minus 4m2l
)
F7F9
)
(318c)
minus(
F2F10q2 +
(
q2 minus 4m2l
)
F6F9
)
m3B
(
m2B minusm2
Klowast
2minus q2
)
P TN = F13
(
8m2l λCTE
(
F8q2 minusF6m
2B minusF7
(
m2Klowast
2minusm2
B
))
+ 4mlmBλCTEF10q2)
+F12
(
16m2lCTE
(
F6m2BminusF7
(
m2Bminusm2
Klowast
2
)
minusF8q2minusmB
2mlF10q
2
)
(
m2Bminusm2
Klowast
2minusq2
)
+ 6(
4m2l + q2
)
CTEF1q2m2
Klowast
2+ 3
(
q2 minus 4m2)
CTF5q2m2
Klowast
2
)
+F11
(
minus16m2lCTE
(
F8q2 + F7
(
m2B minusm2
Klowast
2
)
+mB
2mlF10q
2
)
(
m2B + 3m2
Klowast
2minus q2
)
+6m2Klowast
2
(
4m2l + q2
)
(
CTEF1
(
m2B minusm2
Klowast
2
)
minus CTF2m2B
)
+3(
4m2l minus q2
)
CTF5m2Klowast
2
(
m2Klowast
2minusm2
B
)
+4CTEF6m2B
(
4m2l
(
m2B + 6m2
Klowast
2minus q2
)
minus 3q2m2Klowast
2
)
)
(318d)
and the transverse one is given by
PT propiπλq2u(q2)
12mBm2Klowast
2
λCTEF13
(
4F2m2B minus 3F5m
2Klowast
2+ F3
(
q2 minus 5m2B +m2
Klowast
2
))
(319)
minus2F12
(
2CTE
((
8F3m2B minus (2F3 + 3F5)m
2Klowast
2
)
q2 + 4F2m2B
(
2m2B +m2
Klowast
2minus 2q2
)
minus(
m2Bminusm2
Klowast
2
)(
8F3m2B + (4F3 + 3F5)m
2Klowast
2
))
minus3CTF1m2Klowast
2
(
q2minus3m2B + 3m2
Klowast
2
))
+2F11
(
2CTE
(
3F5m2Klowast
2
(
3m2B +m2
Klowast
2minus q2
)
minus 4F2
(
2m2B + 3m2
Klowast
2minus 2q2
)
m2B
+2F3
(
7m2Klowast
2q2minus4q4+6λ+4m2
B
(
q2+5m2Klowast
2
)))
minus3CTF1m2Klowast
2
(
3m2B+m2
Klowast
2minusq2
)
34 Helicity fractions
Helicity fraction is an observable associated with polarization of the out going meson that
is almost free of hadronic uncertainties The spin-2 polarization tensor which satisfies
ǫmicroνkν = 0 with k being the momentum is symmetric and traceless It can be constructed
by the vector polarization ǫmicro as
ǫmicroν(plusmn2) = ǫmicro(plusmn)ǫν(plusmn) ǫmicroν(plusmn1) =1radic2[ǫmicro(plusmn)ǫν(0) + ǫmicro(0)ǫν(plusmn)]
ǫmicroν(0) =1radic6[ǫmicro(+)ǫν(minus) + ǫmicro(minus)ǫν(+)] +
radic
2
3ǫmicro(0)ǫν(0) (320)
ndash 12 ndash
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
F10 =
[
2(RP minusRprimeP )
mKlowast
mbA0(q
2)
]
F11 = minus2T1(q2)
F12 =
[
2(m2B minusm2
Klowast)
q2(T1(q
2)minus T2(q2))
]
F13 =
[
4
q2
(
T1(q2)minus T2(q
2)minus q2T3(q2)
m2B minusm2
Klowast
)]
(33)
31 Differential decay rate
The differential decay width of B rarr Klowast2 (1430)micro
+microminus in dilepton center of mass frame can
be written as
dΓ(B rarr Klowast2 (1430)micro
+microminus)
dq2=
1
(2π)31
32m3B
int u(q2)
minusu(q2)|MBrarrKlowast
2(1430)micro+microminus |2du (34)
where u = (p + pmicrominus)2 minus (p + pmicro+)2 = u(q2) cos θ and q2 = (pmicro+ + pmicrominus)2 p k pmicro+ and
pmicrominus are the four-momenta vectors of B Klowast2 (1430) micro
+ and microminus respectively and u(q2) are
given by
u(q2) =radic
m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2
radic
1minus 4m2l
q2(35)
Collecting everything together one can write the general expression of the differential decay
rate for B rarr Klowast2 (1430)micro
+microminus as
dΓ
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
18m2lm
4T q
2
3F21m
2Klowast
2q2λ+ 2F2
2m4B(λ+ 10m2
T q2) (36)
+2F23λ
2] (
2m2l + q2
)
minus[
3F25m
2Klowast
2minus 3F2
9m2B
]
K2q2λ+ 12F2
8m2l q
4λ
+2F26m
4B
[
2(
λminus 20m2T q
2)
m2l + q2
(
λ+ 10m2T q
2)]
+ 3F210m
2Bq
4λ
+2F27λ
[
2(
λminus 3q4 + 6m2T q
2)
m2Klowast
2+ q2λ
]
minus 4F2F3m4B
(
2m2l + q2
)
K1λ2
minus4F6F7m2Bλ
[
2(
K1 + 3q2)
m2l +K1q
2]
minus 24F6F8m2lm
2Bq
2λminus 12F10F6mlm3Bq
2λ
+24F7F8m2lK0q
2λ+ 12F10F7mlmBK0q2λ+ 8F11F12q
2(λ+ 10m2Tm
2B minus 10m4
T )K3
minus4F11F13(K1 + 4m2T )λq
2K3 minus 72F1F11mlm2Klowast
2q2λCT
+48F11F2mlm2Bq
2(λ+ 10m2Tm
2B minus 10m4
T )CTE minus 4F12F13K1λq2K3
+48F12F2mlm2Bq
2(
λ+ 10m2T q
2)
CTE minus 48F12F3mlq2K1CTEλ
minus24F13F2mlm2BK1λq
2CTE + 24F13F3mlq2CTEλ
2
where ml is the mass of final state muon and
λ = λ(
m2Bm
2Klowast
2 q2
)
equiv m4B +m4
Klowast
2+ q4 minus 2m2
Klowast
2m2
B minus 2q2m2B minus 2m2
Klowast
2q2 (37)
K0 = (m2B minusm2
Klowast
2) K1 =
(
m2B minusm2
Klowast
2minus q2
)
K2 = q2 minus 4m2l
K3 = q2C2T minus 4m2
l
(
C2T minus 36C2
TE
)
(38)
and the auxiliary functions are the same as defined in eq (33)
ndash 9 ndash
JHEP02(2012)045
32 Forward-backward asymmetry
Now we are in a position to explore the forward-backward asymmetry of final state leptons
in the B rarr Klowast2 (1430)micro
+microminus which is an essential observable sensitive to the new physics
effects To calculate the forward-backward asymmetry we consider the following double
differential decay rate formula for the process B rarr Klowast2 (1430)micro
+microminus
d2Γ(q2 cos θ)
dq2d cos θ=
1
(2π)31
64m3B
u(q2)|MBrarrKlowast
2(1430)micro+microminus |2 (39)
where θ is the angle between the momentum of B baryon and lminus in the dilepton rest frame
The differential and normalized FBAs for the semi-leptonic decay B rarr Klowast2 (1430)l
+lminus are
defined as
dAFB(q2)
dq2=
int 1
0d cos θ
d2Γ(q2 cos θ)
dq2d cos θminusint 0
minus1d cos θ
d2Γ(q2 cos θ)
dq2d cos θ(310)
and
AFB(q2) =
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θminusint 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θ+int 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
(311)
Following the same procedure as we did for the differential decay rate one can easily get
the expression for the forward-backward asymmetry as follows
dAFB(q2)
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
6mBm4T
[
AV AFB +ASP
FB +ATSPFB +AT
FB
]
(312a)
AV AFB = minus3(F2F5 + F1F6)q
2m2Bm
2K2
(312b)
ASPFB = 2F9mlmB
(
F3λ+ F2m2B
[
q2 minusm2B +m2
K2
])
(312c)
ATSPFB = minusq2 (F10CT + 2F9CTE)mB
(
2F12
(
m2B minusm2
K2minus q2
)
(312d)
minusF13λ+ 2F11
(
m2B + 3m2
K2minus q2
))
ATFB = minus2ml
(
12F12F5q2CTEm
2K2
+ 12F11F5CTEm2K2
(
m2B minusm2
K2
)
(312e)
+F13λCT
(
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F12CT
(
m2B minusm2
K2minus q2
) (
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F11CT
(
F6m2B
(
m2B + 9m2
K2minus q2
)
minus(
m2B + 3m2
K2minus q2
) (
F8q2 + F7
(
m2B minusm2
K2
)))
and the expression of the differential decay rate is given in eq (36)
33 Lepton polarization asymmetries
In the rest frame of the lepton microminus the unit vectors along longitudinal normal and transver-
sal component of the microminus can be defined as [55]
sminusmicroL = (0 ~eL) =
(
0~pminus|~pminus|
)
sminusmicroN = (0 ~eN ) =
0~k times ~pminus∣
∣
∣
~k times ~pminus∣
∣
∣
(313)
sminusmicroT = (0 ~eT ) = (0 ~eN times ~eL)
ndash 10 ndash
JHEP02(2012)045
where ~pminus and ~k are the three-momenta of the microminus and Klowast2 (1430) meson respectively in the
center mass (CM) frame of micro+microminus system Lorentz transformation is used to boost the
longitudinal component of the lepton polarization to the CM frame of the lepton pair as
(
sminusmicroL
)
CM=
( |~pminus|ml
El~pminusml |~pminus|
)
(314)
where El and ml are the energy and mass of the final state muon The normal and
transverse components remain unchanged under the Lorentz boost The longitudinal (PL)
normal (PN ) and transverse (PT ) polarizations of lepton can be defined as
P(∓)i (q2) =
dΓdq2
(~ξ∓ = ~e∓)minus dΓdq2
(~ξ∓ = minus~e∓)dΓdq2
(~ξ∓ = ~e∓) + dΓdq2
(~ξ∓ = minus~e∓)(315)
where i = L N T and ~ξ∓ is the spin direction along the leptons micro∓ The differential
decay rate for polarized lepton l∓ in B rarr Klowast2 (1430)micro
+microminus decay along any spin direction~ξ∓ is related to the unpolarized decay rate (36) with the following relation
dΓ(~ξ∓)
dq2=
1
2
(
dΓ
dq2
)
[1 + (P∓L ~e∓L + P∓
N~e∓N + P∓T ~e∓T ) middot ~ξ∓] (316)
We can achieve the expressions of longitudinal normal and transverse polarizations for
B rarr Klowast2 (1430)micro
+microminus decays as collected below The longitudinal lepton polarization can
be written as
PL prop1
36m2Bm
4T
4u(q2)radicλ[
P V AL + PSP
L + P TL
]
(317a)
P V AL = ml
(
2λF2 (F6 minusF7)m4B +
(
3λF1F5q2 + 2F2m
2B
(
10q2F6m2B + λF7
))
m2Klowast
2
+2λF3
(
F6
(
q2 minusm2B +m2
Klowast
2
)
m2B + λF7
))
(317b)
PSPL = 3mlλF9mB
(
minus2mlF8q2 minusF10mBq
2 + 2ml
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
(317c)
P TL = m2
lF11
(
24 (CTEF1 minus CTF5)m2Klowast
2λ+ 4CTλF3
(
m2B + 3m2
Klowast
2minus q2
)
+4m2B (4CTEF6 minus CTF2)
(
10(
m2B minusm2
Klowast
2
)
m2Klowast
2+ λ
))
+m2lF12
(
4m2B (4CTEF6 minus CTF2)
(
10q2m2Klowast
2+ λ
)
minus 4CTF3
(
q2 minusm2B +m2
Klowast
2
))
+m2lF13
(
2CTλminus 4CTF2m2B
(
m2B minusm2
Klowast
2minus q2
)
minus 2CTλ2F3
)
(317d)
ndash 11 ndash
JHEP02(2012)045
Similarly the normal lepton polarization is
PN prop minusπu(q2)t
(12m2Bm
4T
(λ
t)32
[
P V AN + PSP
N + P TN
]
(318a)
P V AN = 2ml
(
F2
(
F8q4 minus
(
(F6 minusF7 + F8)m2B + (minus3F1 + F7 minusF8)m
2Klowast
2
)
q2 (318b)
+(
m2B minusm2
Klowast
2
)
m2B
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
+ λF3
(
F8q2 minusF6m
2B + F7
(
m2B minusm2
Klowast
2
)))
PSPN = mBλ
(
F3F10q2 +
(
q2 minus 4m2l
)
F7F9
)
(318c)
minus(
F2F10q2 +
(
q2 minus 4m2l
)
F6F9
)
m3B
(
m2B minusm2
Klowast
2minus q2
)
P TN = F13
(
8m2l λCTE
(
F8q2 minusF6m
2B minusF7
(
m2Klowast
2minusm2
B
))
+ 4mlmBλCTEF10q2)
+F12
(
16m2lCTE
(
F6m2BminusF7
(
m2Bminusm2
Klowast
2
)
minusF8q2minusmB
2mlF10q
2
)
(
m2Bminusm2
Klowast
2minusq2
)
+ 6(
4m2l + q2
)
CTEF1q2m2
Klowast
2+ 3
(
q2 minus 4m2)
CTF5q2m2
Klowast
2
)
+F11
(
minus16m2lCTE
(
F8q2 + F7
(
m2B minusm2
Klowast
2
)
+mB
2mlF10q
2
)
(
m2B + 3m2
Klowast
2minus q2
)
+6m2Klowast
2
(
4m2l + q2
)
(
CTEF1
(
m2B minusm2
Klowast
2
)
minus CTF2m2B
)
+3(
4m2l minus q2
)
CTF5m2Klowast
2
(
m2Klowast
2minusm2
B
)
+4CTEF6m2B
(
4m2l
(
m2B + 6m2
Klowast
2minus q2
)
minus 3q2m2Klowast
2
)
)
(318d)
and the transverse one is given by
PT propiπλq2u(q2)
12mBm2Klowast
2
λCTEF13
(
4F2m2B minus 3F5m
2Klowast
2+ F3
(
q2 minus 5m2B +m2
Klowast
2
))
(319)
minus2F12
(
2CTE
((
8F3m2B minus (2F3 + 3F5)m
2Klowast
2
)
q2 + 4F2m2B
(
2m2B +m2
Klowast
2minus 2q2
)
minus(
m2Bminusm2
Klowast
2
)(
8F3m2B + (4F3 + 3F5)m
2Klowast
2
))
minus3CTF1m2Klowast
2
(
q2minus3m2B + 3m2
Klowast
2
))
+2F11
(
2CTE
(
3F5m2Klowast
2
(
3m2B +m2
Klowast
2minus q2
)
minus 4F2
(
2m2B + 3m2
Klowast
2minus 2q2
)
m2B
+2F3
(
7m2Klowast
2q2minus4q4+6λ+4m2
B
(
q2+5m2Klowast
2
)))
minus3CTF1m2Klowast
2
(
3m2B+m2
Klowast
2minusq2
)
34 Helicity fractions
Helicity fraction is an observable associated with polarization of the out going meson that
is almost free of hadronic uncertainties The spin-2 polarization tensor which satisfies
ǫmicroνkν = 0 with k being the momentum is symmetric and traceless It can be constructed
by the vector polarization ǫmicro as
ǫmicroν(plusmn2) = ǫmicro(plusmn)ǫν(plusmn) ǫmicroν(plusmn1) =1radic2[ǫmicro(plusmn)ǫν(0) + ǫmicro(0)ǫν(plusmn)]
ǫmicroν(0) =1radic6[ǫmicro(+)ǫν(minus) + ǫmicro(minus)ǫν(+)] +
radic
2
3ǫmicro(0)ǫν(0) (320)
ndash 12 ndash
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
32 Forward-backward asymmetry
Now we are in a position to explore the forward-backward asymmetry of final state leptons
in the B rarr Klowast2 (1430)micro
+microminus which is an essential observable sensitive to the new physics
effects To calculate the forward-backward asymmetry we consider the following double
differential decay rate formula for the process B rarr Klowast2 (1430)micro
+microminus
d2Γ(q2 cos θ)
dq2d cos θ=
1
(2π)31
64m3B
u(q2)|MBrarrKlowast
2(1430)micro+microminus |2 (39)
where θ is the angle between the momentum of B baryon and lminus in the dilepton rest frame
The differential and normalized FBAs for the semi-leptonic decay B rarr Klowast2 (1430)l
+lminus are
defined as
dAFB(q2)
dq2=
int 1
0d cos θ
d2Γ(q2 cos θ)
dq2d cos θminusint 0
minus1d cos θ
d2Γ(q2 cos θ)
dq2d cos θ(310)
and
AFB(q2) =
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θminusint 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
int 10 d cos θ d2Γ(q2cos θ)
dq2d cos θ+int 0minus1 d cos θ
d2Γ(q2cos θ)dq2d cos θ
(311)
Following the same procedure as we did for the differential decay rate one can easily get
the expression for the forward-backward asymmetry as follows
dAFB(q2)
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2
u(q2)λ
6mBm4T
[
AV AFB +ASP
FB +ATSPFB +AT
FB
]
(312a)
AV AFB = minus3(F2F5 + F1F6)q
2m2Bm
2K2
(312b)
ASPFB = 2F9mlmB
(
F3λ+ F2m2B
[
q2 minusm2B +m2
K2
])
(312c)
ATSPFB = minusq2 (F10CT + 2F9CTE)mB
(
2F12
(
m2B minusm2
K2minus q2
)
(312d)
minusF13λ+ 2F11
(
m2B + 3m2
K2minus q2
))
ATFB = minus2ml
(
12F12F5q2CTEm
2K2
+ 12F11F5CTEm2K2
(
m2B minusm2
K2
)
(312e)
+F13λCT
(
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F12CT
(
m2B minusm2
K2minus q2
) (
(F6 minusF7)m2B minusF8q
2 + F7m2K2
)
minus2F11CT
(
F6m2B
(
m2B + 9m2
K2minus q2
)
minus(
m2B + 3m2
K2minus q2
) (
F8q2 + F7
(
m2B minusm2
K2
)))
and the expression of the differential decay rate is given in eq (36)
33 Lepton polarization asymmetries
In the rest frame of the lepton microminus the unit vectors along longitudinal normal and transver-
sal component of the microminus can be defined as [55]
sminusmicroL = (0 ~eL) =
(
0~pminus|~pminus|
)
sminusmicroN = (0 ~eN ) =
0~k times ~pminus∣
∣
∣
~k times ~pminus∣
∣
∣
(313)
sminusmicroT = (0 ~eT ) = (0 ~eN times ~eL)
ndash 10 ndash
JHEP02(2012)045
where ~pminus and ~k are the three-momenta of the microminus and Klowast2 (1430) meson respectively in the
center mass (CM) frame of micro+microminus system Lorentz transformation is used to boost the
longitudinal component of the lepton polarization to the CM frame of the lepton pair as
(
sminusmicroL
)
CM=
( |~pminus|ml
El~pminusml |~pminus|
)
(314)
where El and ml are the energy and mass of the final state muon The normal and
transverse components remain unchanged under the Lorentz boost The longitudinal (PL)
normal (PN ) and transverse (PT ) polarizations of lepton can be defined as
P(∓)i (q2) =
dΓdq2
(~ξ∓ = ~e∓)minus dΓdq2
(~ξ∓ = minus~e∓)dΓdq2
(~ξ∓ = ~e∓) + dΓdq2
(~ξ∓ = minus~e∓)(315)
where i = L N T and ~ξ∓ is the spin direction along the leptons micro∓ The differential
decay rate for polarized lepton l∓ in B rarr Klowast2 (1430)micro
+microminus decay along any spin direction~ξ∓ is related to the unpolarized decay rate (36) with the following relation
dΓ(~ξ∓)
dq2=
1
2
(
dΓ
dq2
)
[1 + (P∓L ~e∓L + P∓
N~e∓N + P∓T ~e∓T ) middot ~ξ∓] (316)
We can achieve the expressions of longitudinal normal and transverse polarizations for
B rarr Klowast2 (1430)micro
+microminus decays as collected below The longitudinal lepton polarization can
be written as
PL prop1
36m2Bm
4T
4u(q2)radicλ[
P V AL + PSP
L + P TL
]
(317a)
P V AL = ml
(
2λF2 (F6 minusF7)m4B +
(
3λF1F5q2 + 2F2m
2B
(
10q2F6m2B + λF7
))
m2Klowast
2
+2λF3
(
F6
(
q2 minusm2B +m2
Klowast
2
)
m2B + λF7
))
(317b)
PSPL = 3mlλF9mB
(
minus2mlF8q2 minusF10mBq
2 + 2ml
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
(317c)
P TL = m2
lF11
(
24 (CTEF1 minus CTF5)m2Klowast
2λ+ 4CTλF3
(
m2B + 3m2
Klowast
2minus q2
)
+4m2B (4CTEF6 minus CTF2)
(
10(
m2B minusm2
Klowast
2
)
m2Klowast
2+ λ
))
+m2lF12
(
4m2B (4CTEF6 minus CTF2)
(
10q2m2Klowast
2+ λ
)
minus 4CTF3
(
q2 minusm2B +m2
Klowast
2
))
+m2lF13
(
2CTλminus 4CTF2m2B
(
m2B minusm2
Klowast
2minus q2
)
minus 2CTλ2F3
)
(317d)
ndash 11 ndash
JHEP02(2012)045
Similarly the normal lepton polarization is
PN prop minusπu(q2)t
(12m2Bm
4T
(λ
t)32
[
P V AN + PSP
N + P TN
]
(318a)
P V AN = 2ml
(
F2
(
F8q4 minus
(
(F6 minusF7 + F8)m2B + (minus3F1 + F7 minusF8)m
2Klowast
2
)
q2 (318b)
+(
m2B minusm2
Klowast
2
)
m2B
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
+ λF3
(
F8q2 minusF6m
2B + F7
(
m2B minusm2
Klowast
2
)))
PSPN = mBλ
(
F3F10q2 +
(
q2 minus 4m2l
)
F7F9
)
(318c)
minus(
F2F10q2 +
(
q2 minus 4m2l
)
F6F9
)
m3B
(
m2B minusm2
Klowast
2minus q2
)
P TN = F13
(
8m2l λCTE
(
F8q2 minusF6m
2B minusF7
(
m2Klowast
2minusm2
B
))
+ 4mlmBλCTEF10q2)
+F12
(
16m2lCTE
(
F6m2BminusF7
(
m2Bminusm2
Klowast
2
)
minusF8q2minusmB
2mlF10q
2
)
(
m2Bminusm2
Klowast
2minusq2
)
+ 6(
4m2l + q2
)
CTEF1q2m2
Klowast
2+ 3
(
q2 minus 4m2)
CTF5q2m2
Klowast
2
)
+F11
(
minus16m2lCTE
(
F8q2 + F7
(
m2B minusm2
Klowast
2
)
+mB
2mlF10q
2
)
(
m2B + 3m2
Klowast
2minus q2
)
+6m2Klowast
2
(
4m2l + q2
)
(
CTEF1
(
m2B minusm2
Klowast
2
)
minus CTF2m2B
)
+3(
4m2l minus q2
)
CTF5m2Klowast
2
(
m2Klowast
2minusm2
B
)
+4CTEF6m2B
(
4m2l
(
m2B + 6m2
Klowast
2minus q2
)
minus 3q2m2Klowast
2
)
)
(318d)
and the transverse one is given by
PT propiπλq2u(q2)
12mBm2Klowast
2
λCTEF13
(
4F2m2B minus 3F5m
2Klowast
2+ F3
(
q2 minus 5m2B +m2
Klowast
2
))
(319)
minus2F12
(
2CTE
((
8F3m2B minus (2F3 + 3F5)m
2Klowast
2
)
q2 + 4F2m2B
(
2m2B +m2
Klowast
2minus 2q2
)
minus(
m2Bminusm2
Klowast
2
)(
8F3m2B + (4F3 + 3F5)m
2Klowast
2
))
minus3CTF1m2Klowast
2
(
q2minus3m2B + 3m2
Klowast
2
))
+2F11
(
2CTE
(
3F5m2Klowast
2
(
3m2B +m2
Klowast
2minus q2
)
minus 4F2
(
2m2B + 3m2
Klowast
2minus 2q2
)
m2B
+2F3
(
7m2Klowast
2q2minus4q4+6λ+4m2
B
(
q2+5m2Klowast
2
)))
minus3CTF1m2Klowast
2
(
3m2B+m2
Klowast
2minusq2
)
34 Helicity fractions
Helicity fraction is an observable associated with polarization of the out going meson that
is almost free of hadronic uncertainties The spin-2 polarization tensor which satisfies
ǫmicroνkν = 0 with k being the momentum is symmetric and traceless It can be constructed
by the vector polarization ǫmicro as
ǫmicroν(plusmn2) = ǫmicro(plusmn)ǫν(plusmn) ǫmicroν(plusmn1) =1radic2[ǫmicro(plusmn)ǫν(0) + ǫmicro(0)ǫν(plusmn)]
ǫmicroν(0) =1radic6[ǫmicro(+)ǫν(minus) + ǫmicro(minus)ǫν(+)] +
radic
2
3ǫmicro(0)ǫν(0) (320)
ndash 12 ndash
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
where ~pminus and ~k are the three-momenta of the microminus and Klowast2 (1430) meson respectively in the
center mass (CM) frame of micro+microminus system Lorentz transformation is used to boost the
longitudinal component of the lepton polarization to the CM frame of the lepton pair as
(
sminusmicroL
)
CM=
( |~pminus|ml
El~pminusml |~pminus|
)
(314)
where El and ml are the energy and mass of the final state muon The normal and
transverse components remain unchanged under the Lorentz boost The longitudinal (PL)
normal (PN ) and transverse (PT ) polarizations of lepton can be defined as
P(∓)i (q2) =
dΓdq2
(~ξ∓ = ~e∓)minus dΓdq2
(~ξ∓ = minus~e∓)dΓdq2
(~ξ∓ = ~e∓) + dΓdq2
(~ξ∓ = minus~e∓)(315)
where i = L N T and ~ξ∓ is the spin direction along the leptons micro∓ The differential
decay rate for polarized lepton l∓ in B rarr Klowast2 (1430)micro
+microminus decay along any spin direction~ξ∓ is related to the unpolarized decay rate (36) with the following relation
dΓ(~ξ∓)
dq2=
1
2
(
dΓ
dq2
)
[1 + (P∓L ~e∓L + P∓
N~e∓N + P∓T ~e∓T ) middot ~ξ∓] (316)
We can achieve the expressions of longitudinal normal and transverse polarizations for
B rarr Klowast2 (1430)micro
+microminus decays as collected below The longitudinal lepton polarization can
be written as
PL prop1
36m2Bm
4T
4u(q2)radicλ[
P V AL + PSP
L + P TL
]
(317a)
P V AL = ml
(
2λF2 (F6 minusF7)m4B +
(
3λF1F5q2 + 2F2m
2B
(
10q2F6m2B + λF7
))
m2Klowast
2
+2λF3
(
F6
(
q2 minusm2B +m2
Klowast
2
)
m2B + λF7
))
(317b)
PSPL = 3mlλF9mB
(
minus2mlF8q2 minusF10mBq
2 + 2ml
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
(317c)
P TL = m2
lF11
(
24 (CTEF1 minus CTF5)m2Klowast
2λ+ 4CTλF3
(
m2B + 3m2
Klowast
2minus q2
)
+4m2B (4CTEF6 minus CTF2)
(
10(
m2B minusm2
Klowast
2
)
m2Klowast
2+ λ
))
+m2lF12
(
4m2B (4CTEF6 minus CTF2)
(
10q2m2Klowast
2+ λ
)
minus 4CTF3
(
q2 minusm2B +m2
Klowast
2
))
+m2lF13
(
2CTλminus 4CTF2m2B
(
m2B minusm2
Klowast
2minus q2
)
minus 2CTλ2F3
)
(317d)
ndash 11 ndash
JHEP02(2012)045
Similarly the normal lepton polarization is
PN prop minusπu(q2)t
(12m2Bm
4T
(λ
t)32
[
P V AN + PSP
N + P TN
]
(318a)
P V AN = 2ml
(
F2
(
F8q4 minus
(
(F6 minusF7 + F8)m2B + (minus3F1 + F7 minusF8)m
2Klowast
2
)
q2 (318b)
+(
m2B minusm2
Klowast
2
)
m2B
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
+ λF3
(
F8q2 minusF6m
2B + F7
(
m2B minusm2
Klowast
2
)))
PSPN = mBλ
(
F3F10q2 +
(
q2 minus 4m2l
)
F7F9
)
(318c)
minus(
F2F10q2 +
(
q2 minus 4m2l
)
F6F9
)
m3B
(
m2B minusm2
Klowast
2minus q2
)
P TN = F13
(
8m2l λCTE
(
F8q2 minusF6m
2B minusF7
(
m2Klowast
2minusm2
B
))
+ 4mlmBλCTEF10q2)
+F12
(
16m2lCTE
(
F6m2BminusF7
(
m2Bminusm2
Klowast
2
)
minusF8q2minusmB
2mlF10q
2
)
(
m2Bminusm2
Klowast
2minusq2
)
+ 6(
4m2l + q2
)
CTEF1q2m2
Klowast
2+ 3
(
q2 minus 4m2)
CTF5q2m2
Klowast
2
)
+F11
(
minus16m2lCTE
(
F8q2 + F7
(
m2B minusm2
Klowast
2
)
+mB
2mlF10q
2
)
(
m2B + 3m2
Klowast
2minus q2
)
+6m2Klowast
2
(
4m2l + q2
)
(
CTEF1
(
m2B minusm2
Klowast
2
)
minus CTF2m2B
)
+3(
4m2l minus q2
)
CTF5m2Klowast
2
(
m2Klowast
2minusm2
B
)
+4CTEF6m2B
(
4m2l
(
m2B + 6m2
Klowast
2minus q2
)
minus 3q2m2Klowast
2
)
)
(318d)
and the transverse one is given by
PT propiπλq2u(q2)
12mBm2Klowast
2
λCTEF13
(
4F2m2B minus 3F5m
2Klowast
2+ F3
(
q2 minus 5m2B +m2
Klowast
2
))
(319)
minus2F12
(
2CTE
((
8F3m2B minus (2F3 + 3F5)m
2Klowast
2
)
q2 + 4F2m2B
(
2m2B +m2
Klowast
2minus 2q2
)
minus(
m2Bminusm2
Klowast
2
)(
8F3m2B + (4F3 + 3F5)m
2Klowast
2
))
minus3CTF1m2Klowast
2
(
q2minus3m2B + 3m2
Klowast
2
))
+2F11
(
2CTE
(
3F5m2Klowast
2
(
3m2B +m2
Klowast
2minus q2
)
minus 4F2
(
2m2B + 3m2
Klowast
2minus 2q2
)
m2B
+2F3
(
7m2Klowast
2q2minus4q4+6λ+4m2
B
(
q2+5m2Klowast
2
)))
minus3CTF1m2Klowast
2
(
3m2B+m2
Klowast
2minusq2
)
34 Helicity fractions
Helicity fraction is an observable associated with polarization of the out going meson that
is almost free of hadronic uncertainties The spin-2 polarization tensor which satisfies
ǫmicroνkν = 0 with k being the momentum is symmetric and traceless It can be constructed
by the vector polarization ǫmicro as
ǫmicroν(plusmn2) = ǫmicro(plusmn)ǫν(plusmn) ǫmicroν(plusmn1) =1radic2[ǫmicro(plusmn)ǫν(0) + ǫmicro(0)ǫν(plusmn)]
ǫmicroν(0) =1radic6[ǫmicro(+)ǫν(minus) + ǫmicro(minus)ǫν(+)] +
radic
2
3ǫmicro(0)ǫν(0) (320)
ndash 12 ndash
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
Similarly the normal lepton polarization is
PN prop minusπu(q2)t
(12m2Bm
4T
(λ
t)32
[
P V AN + PSP
N + P TN
]
(318a)
P V AN = 2ml
(
F2
(
F8q4 minus
(
(F6 minusF7 + F8)m2B + (minus3F1 + F7 minusF8)m
2Klowast
2
)
q2 (318b)
+(
m2B minusm2
Klowast
2
)
m2B
(
(F6 minusF7)m2B + F7m
2Klowast
2
))
+ λF3
(
F8q2 minusF6m
2B + F7
(
m2B minusm2
Klowast
2
)))
PSPN = mBλ
(
F3F10q2 +
(
q2 minus 4m2l
)
F7F9
)
(318c)
minus(
F2F10q2 +
(
q2 minus 4m2l
)
F6F9
)
m3B
(
m2B minusm2
Klowast
2minus q2
)
P TN = F13
(
8m2l λCTE
(
F8q2 minusF6m
2B minusF7
(
m2Klowast
2minusm2
B
))
+ 4mlmBλCTEF10q2)
+F12
(
16m2lCTE
(
F6m2BminusF7
(
m2Bminusm2
Klowast
2
)
minusF8q2minusmB
2mlF10q
2
)
(
m2Bminusm2
Klowast
2minusq2
)
+ 6(
4m2l + q2
)
CTEF1q2m2
Klowast
2+ 3
(
q2 minus 4m2)
CTF5q2m2
Klowast
2
)
+F11
(
minus16m2lCTE
(
F8q2 + F7
(
m2B minusm2
Klowast
2
)
+mB
2mlF10q
2
)
(
m2B + 3m2
Klowast
2minus q2
)
+6m2Klowast
2
(
4m2l + q2
)
(
CTEF1
(
m2B minusm2
Klowast
2
)
minus CTF2m2B
)
+3(
4m2l minus q2
)
CTF5m2Klowast
2
(
m2Klowast
2minusm2
B
)
+4CTEF6m2B
(
4m2l
(
m2B + 6m2
Klowast
2minus q2
)
minus 3q2m2Klowast
2
)
)
(318d)
and the transverse one is given by
PT propiπλq2u(q2)
12mBm2Klowast
2
λCTEF13
(
4F2m2B minus 3F5m
2Klowast
2+ F3
(
q2 minus 5m2B +m2
Klowast
2
))
(319)
minus2F12
(
2CTE
((
8F3m2B minus (2F3 + 3F5)m
2Klowast
2
)
q2 + 4F2m2B
(
2m2B +m2
Klowast
2minus 2q2
)
minus(
m2Bminusm2
Klowast
2
)(
8F3m2B + (4F3 + 3F5)m
2Klowast
2
))
minus3CTF1m2Klowast
2
(
q2minus3m2B + 3m2
Klowast
2
))
+2F11
(
2CTE
(
3F5m2Klowast
2
(
3m2B +m2
Klowast
2minus q2
)
minus 4F2
(
2m2B + 3m2
Klowast
2minus 2q2
)
m2B
+2F3
(
7m2Klowast
2q2minus4q4+6λ+4m2
B
(
q2+5m2Klowast
2
)))
minus3CTF1m2Klowast
2
(
3m2B+m2
Klowast
2minusq2
)
34 Helicity fractions
Helicity fraction is an observable associated with polarization of the out going meson that
is almost free of hadronic uncertainties The spin-2 polarization tensor which satisfies
ǫmicroνkν = 0 with k being the momentum is symmetric and traceless It can be constructed
by the vector polarization ǫmicro as
ǫmicroν(plusmn2) = ǫmicro(plusmn)ǫν(plusmn) ǫmicroν(plusmn1) =1radic2[ǫmicro(plusmn)ǫν(0) + ǫmicro(0)ǫν(plusmn)]
ǫmicroν(0) =1radic6[ǫmicro(+)ǫν(minus) + ǫmicro(minus)ǫν(+)] +
radic
2
3ǫmicro(0)ǫν(0) (320)
ndash 12 ndash
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
using the definition
εTν(n) =ενα(n)p
α
mB
the above relations simplify to
εTν(plusmn2) = 0 εTν(plusmn1) =ǫ(0)pradic2mB
ǫmicro(plusmn) εTν(0) =
radic
2
3
ǫ(0)p
mBǫmicro(0)
The physical expressions for helicity fractions are given by
fi(q2) =
dΓidq2
dΓdq2 i = L T (321)
Here L and T refers to longitudinal and transverse helicity fractions The explicit expression
of the longitudinal helicity fraction for the decay B rarr Klowast2 (1430)l
+lminus is
dΓL
dq2=
G2Fα
2
211π5m3B
|VtbVlowastts|2 u(q2)
36m4Klowast
2m2
Bq2
(
4F 22m
4B
(
2m2 + q2)
K21 + 4F 2
3 (2m2 + t)λ2
+6F 29 q
2λm2B
(
q2 minus 4m)
+ 6F 210q
4λm2B + 4F 2
6m4B
(
q2K21 + 2m2
(
λminus 8q2m2Klowast
2
))
+4F 27 λ
(
2m2(
4q2(
m2B +m2
Klowast
2
)
+K20 minus 2q4
)
+ q2λ)
+ 24F 28m
2q4λ
minus8F6F7λm2B
(
2m2(
K0 + 2q2)
+ q2K1
)
minus 8F2F3λm2B
(
2m2 + q2)
K1 minus 8F12F13q2λK1K3
+48F7F8m2q2λK0 + 8F 2
11q2K2
4K3 + 8F 212q
2K21K3 + 2F 2
13q2λ2K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+ 48F3F13mq2λ2CTE
minus48F2F13mq2λm2BCTEK1 minus 96F3F12mq2λCTEK1 + 96F2F12mq2m2
BCTEK21
+96F2F11mq2m2BCTEK1K4 minus 48F2F13mq2λm2
BCTEK1 minus 96F3F12mq2λCTEK1
+8F 211q
2K24K3 + 8F 2
12q2K2
1K3 + 2F 213q
2λ2K3 minus 8F12F13q2λK1K3 + 16F11F12q
2K1K4K3
minus8F11F13λ(
4C2Tm
2 (λminusK0K1) + 144m2q2C2TEK4 + 3m2C2
Tm2Klowast
2
)
+96F2F12mq2m2BCTEK
21 +48F3F13mq2λ2CTE + 96F2F11mq2m2
BCTEK1K4
)
(322)
As the sum of the longitudinal and transverse helicity amplitudes is equal to unity ie
fL(q2) + fT (q
2) = 1 for each value of q2 therefore the expression of transverse helicity
fraction of final state meson is quite obvious
4 Numerical Analysis
In this section we will examine the above derived physical observables and analyze the
effects of MI parameters on these observables As B rarr Klowast2 (1430)micro
+microminus is not yet observed
therefore the purpose of this study is not to get constraints on NP parameters but is
to use the constraints on MI parameters defined in section 24 which are coming from
different B meson decays We consider different Lorentz structures of NP as well as
their combinations and examine their implications on differential decay rate the forward-
backward asymmetry the lepton polarization asymmetries and the helicity fractions of the
ndash 13 ndash
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
mB = 528GeV mb = 428GeV ms = 013GeV
mmicro = 0105GeV mτ = 177GeV fB = 025GeV
|VtbVlowastts| = 45times 10minus3 αminus1 = 137 GF = 117times 10minus5GeVminus2
τB = 154times 10minus12 sec mKlowast
2= 143GeV
Table 2 Default values of input parameters used in the calculations [56]
C1 C2 C3 C4 C5 C6 C7 C9 C10
1107 -0248 -0011 -0026 -0007 -0031 -0313 4344 -4669
Table 3 The Wilson coefficients Cmicroi at the scale micro sim mb in the SM [56]
final state Klowast2 (1430) meson Here we varied the strength of individual NP couplings such
that they lies inside the bounds given by different flavor decays (cf section 24) In all the
figures the band correspond to the uncertainties in different input parameters where form
factors (cf table 1) are the major contributors The same type of lines correspond to the
same set of NP parameters and all the NP curves are plotted for the central values of the
form factors and other input parameters To make the quantitative analysis complete the
numerical values of input parameters that we have used are given in table 2 and 3
SemileptonicB decays are ideal probes to study the physics in and beyond the Standard
Model There are a large number of observables which are accessible in these decays The
branching ratio in general for semi-leptonic decays like B rarr Klowast2 (1430)micro
+microminus is prune
to many sources of uncertainties The major source of uncertainty originate from the
B rarr Klowast2 (1430) transition form factors calculated using the LCSR approach as shown in
table 1 can bring about 20 minus 30 uncertainty to the differential branching ratio This
goes to show that differential branching ratio is not a suitable observable to look for the
NP effects unless these effects are very drastic It is therefore valuable to look for the
observables where hadronic uncertainties almost have no effect In this regard the most
important observables are the zero position of the forward-backward asymmetry different
lepton polarization asymmetries and the helicity fractions of the final state meson These
observables are almost free from the hadronic uncertainties and serve as an important
probe to look for NP
The SM predicts the zero crossing of AFB(q2) at a well determined position which is
free from the hadronic uncertainties at the leading order (LO) in strong coupling αs [11ndash13]
This zero position of AFB which is independent of form factors is an important observable
in the search of new physics The short distance relation between the Wilson coefficients
and the zero position of AFB is given by [12 13]
real[Ceff9 (q20)] =
2mbmB
q20Ceff7 (41)
where q20 is the zero position (ZP) of the AFB Recently LHCb has published its results on
AFB(B rarr Klowastmicro+microminus) that are quite close to SM predictions [15] The LHCb result shows
with small error bars that the zero position of AFB(B rarr Klowastmicro+microminus) is close to the SMrsquos
zero position Like B rarr Klowastmicro+microminus decay the semileptonic decay B rarr Klowast2 (1430)micro
+microminus also
ndash 14 ndash
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
occurs through the quark level transition brarr smicro+microminus Therefore the future measurements
of the AFB(B rarr Klowast2 (1430)micro
+microminus) will shed more light on NP in the flavor sector
Now following the lines of B rarr Klowastmicro+microminus decay the semileptonic decay B rarrKlowast
2 (1430)micro+microminus also occurs through the quark level transition b rarr smicro+microminus therefore the
future measurements of the AFB will shed some light on the searches of physics in and
beyond the SM in the flavor sector
The polarization of the final state leptons can shed light on the helicity structure of
the electroweak interactions The longitudinal and normal lepton polarization asymmetry
are also very good observables to look for NP effects As in the case of forward-backward
asymmetry the long distance effects are also canceled out in these asymmetries Hence
they provide a good tool to test the various new physics extensions of the SM In the
present numerical analysis we have taken the NP couplings to be real The transverse
lepton polarization asymmetry as given in eq (319) constitutes of the imaginary part
of the auxiliary functions hence for real couplings its value comes out to be negligibly
small In this numerical study we will discuss the results of transverse lepton polarization
asymmetry in the presence of all NP operators at the very end
Another interesting observable is the study of the spin effects of the final state meson
which for our case is the Klowast2 (1430) meson A detailed discussion about the effects of NP
operators on the longitudinal and transverse helicity fractions of final state meson will also
be done in the forthcoming numerical analysis
A model independent numerical analysis of this decay channel B rarr Klowast2 (1430)micro
+microminus
is presented in this section where we will analyze the effects of different NP operator
couplings (VASPT) on different physical observables A similar NP study was presented
in [46] where the observables studied were polarized branching ratios as function of NP
couplings and forward backward asymmetry The observables we have presented in this
manuscript are different than the ones presented in [46] For example we have studied
differential observables(that are functions of q2) like branching ratio forward backward
asymmetry lepton polarization asymmetries and helicity fractions of the final state meson
We have also incorporated the old bounds [51 52] as well as the new LHCb bound [15]
on different NP couplings We will study the effects of these NP couplings one by one as
follows
41 V A new-physics operators
In this section we shall consider the scenarios when (a) only RVA couplings are present
(b) only RprimeVA couplings are present and (c) both types of couplings are present
Figures 1ndash5 display the results when the only vector-axial vector V A NP couplings
(RVA and RprimeVA) are present In the case of differential branching ratio it can be seen
that its values increase for certain range of parameters while decrease for other range of
parameters The increase in differential branching ratio is up to 4 time its SM value for
the case when both type of NP couplings are present simultaneously (cf figure 1(cd))
As can be seen in figure 2 that the AFB(q2) is very sensitive to the NP effects The zero
crossing is also disturbed significantly by the VA couplings The short distance relation
ndash 15 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
dG
dq2H
Breg
K2 H
1430L+Μ++Μ-L
Figure 1 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of V A couplings inside their allowed region In figure
(a) only RV and RA are present figure (b) when only Rprime
V and Rprime
A are present figure (c) figure (d)
when both RV Rprime
V and RA Rprime
A are present and in all figures the solid line represent the SM with
light green shaded region as uncertainty in SM
eq (41) is modified with the inclusion of new VA couplings which now takes the form
real(Ceff9 (q20)) +RV minus
RprimeV R
primeA
C10=
2mbmB
q20Ceff7 (42)
The experimental results that came in from measurement of AFB(B rarr Klowastmicro+microminus) at
LHCb can put stringent bound on the NP coupling constants In the measurement of the
zero position of AFB(B rarr Klowastmicro+microminus) at LHCb the experimental error bar in this zero
position is roughly 30 percent When this error bar uncertainty is plugged in eq (42) we
get a new bound on the VA coupling constants
minus 1 lt RV minusRprime
V RprimeA
C10lt 32 (43)
When this bound is taken into consideration then the zero position (ZP) stays in the
vicinity of Standard Modelrsquos ZP (see figures 2(abc)) But if we ignore this new bound
then the effects on forward backward asymmetry become very drastic (see figure 2d) These
effects increase when all the couplings RVA and RprimeVA are present (figures 2(cd)) The zero
crossing shifts quite significantly and it even disappears for certain values of RVA and RprimeVA
(figure 2d)
ndash 16 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AF
BH
Breg
K2 H
1430L+Μ++Μ-L
Figure 2 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of V A couplings The caption for the above figures are the same as figure 1
Figures 3 and 4 depict the effects on lepton polarization asymmetries coming from
RVA and RprimeVA couplings The effects are quite obvious in the case of longitudinal lepton
polarization asymmetry The magnitude of PL decrease in most cases and when RprimeVA is
present the effects get more amplified This asymmetry even vanishes (figure 3b) in some
values of RprimeVA couplings When both RVA and Rprime
VA are present PL even changes sign for
some values of couplings(see figures 3(cd)) Seen in eq (317b) the V A effects are only
ml suppressed compared to other NP contributions that are m2l suppressed Qualitatively
these effects are large because of large numerical values and different signs of the new V A
couplings The normal lepton polarization asymmetry is also sensitive to NP effects as it
develops a zero crossing which is not present in SM Still the effects are suppressed by ml
(see eq (318b)) hence in figure 4 all curves show nearly the same behavior
The longitudinal and transverse helicity fractions are depicted in figures 5 The de-
viation from the SM results are fairly large that arise from the effects of different V A
couplings When both RVA and RprimeVA couplings are present (see figures 5(cdgh)) the
traits become even more conspicuous
ndash 17 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-02
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-02
0
02
04
06
08
1
P LH
Breg
K2 H
1430L+Μ++Μ-L
Figure 3 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of V A couplings The caption for the above figures are the same as figure 1
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 4 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of V A couplings The caption for the above figures are the same as figure 1
ndash 18 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f LH
Breg
K2 H
1430L+Μ++Μ-L
(e) (f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(g) (h)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1
f TH
Breg
K2 H
1430L+Μ++Μ-L
Figure 5 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of V A couplings The caption for the above figures
are the same as figure 1
ndash 19 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 6 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of SP couplings inside their allowed region In figure
(a) only RS and RP are present figure (b) when only Rprime
S and Rprime
P are present figure (c) when both
RS Rprime
S and RP Rprime
P are present and in all figures the solid line represent the SM with light green
shaded region as uncertainty in SM
42 SP new-physics operators
In this section we shall consider the scenarios when (a) only RS and RprimeS couplings are
present (b) only RP and RprimeP couplings are present and (c) both types of couplings
are present
The differential branching ratio in figure 6 show that it is slightly disturbed by the
different values of SP parameters Figure 7 depicts that the lepton forward-backward
asymmetry is not very sensitive to the NP arising form SP operators There is a slight
shift in the zero position of the AFB(q2) towards left or right These mild effects can also
be inferred from the eq (312c) that SP effects on forward-backward asymmetry are ml
suppressed
Figure 8 displays the plots of the longitudinal lepton asymmetry in the presence of SP
operator couplings The S and P couplings separately (figures 8(ab)) have a mildly effect
on the longitudinal lepton polarization asymmetry while the effects increase three folds
when both the couplings are present figure 8(c) The dominant contribution comes from
the F9F10 term in eq (317c) which is enhanced by a factor of mBq2
ndash 20 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 7 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of SP couplings The caption for the above figures are the same as figure 6
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 8 The dependence of Longitudinal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of SP couplings The caption for the above figures are the same as figure 6
ndash 21 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
06
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 9 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of SP couplings The caption for the above figures are the same as figure 6
The normal lepton polarization asymmetry is very sensitive to the S and P couplings
In SM this asymmetry takes only negative values and there is no zero crossing but as
S and P couplings are introduced the curves are scattered in both positive and negative
regimes (Fig 9) When both SP couplings are present the effects are even more enhanced
The eq (318c) clearly shows that SP contribution is not ml suppressed like other V A
contributions to the normal polarization asymmetry So the normal lepton polarization
asymmetry is a very good tool to constraint the values of the SP couplings
In case of SP couplings the longitudinal and transverse helicity fractions are shown in
figure 10 The effects in this case are quite subtle especially in the large q2 region as seen
in figure 10 The deviation from SM amplifies when both S and P couplings are present
(see figures 10(cf))
43 T operators and interference of SP and T operators
In this section we shall consider the scenarios when (a) only CT and CTE couplings are
present (b) when S CT and CTE couplings are present and (c) when P CT and CTE
couplings are present
The differential branching ratio shown in figure 11 indicates that its value increases for
most values T coupling parameters These T type coupling also effects the zero crossing of
the AFB(q2) which can be seen in figure 12 By looking at the eq (312) one can see that
ndash 22 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 10 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of SP couplings The caption for the above figures are
the same as figure 6
ndash 23 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 11 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of T-SP couplings inside their allowed region In figure
(a) only CT and CTE are present figure (b) when only CT CTE RS and Rprime
S are present figure
(c) when only CT CTE RP and Rprime
P are present and in all figures the solid line represent the SM
with light green shaded region as uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
0
01
02
03
04
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 12 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of T-SP couplings The caption for the above figures are the same as figure 11
ndash 24 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 13 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
the contribution from the T couplings is ml suppressed (cf eq (312e)) but after including
SP operators along with T operators it is no more ml suppressed It is therefore expected
that the value of AFB(q2) in this scenario will be large compared to T coupling only but
the sever constraints on the SP couplings do not allow AFB(q2) to become significantly
more than the SM in magnitude Also there is some parameter space of couplings where
AFB(q2) is negative every where ie there is no zero crossing (figure 12(bc))
In figure 13(a) the longitudinal lepton asymmetry is shown in the presence of T oper-
ator couplings From eq (317b) we can observe that the effect of the T couplings are m2l
suppressed and therefore we expect the small variation of longitudinal lepton polarization
asymmetry unless the value of T couplings is large and this can also be infer from figure 13
When SP couplings are also included the results hardly change (figure 13(bc)) since there
effect is also ml suppressed compared to SM results
The normal lepton polarization asymmetry (figure 14(a)) develops a zero crossing when
only T operator couplings are incorporated Adding the SP operators change the plots as
well The zero crossing of the normal lepton polarization asymmetry is shifted when the
SP couplings are introduces along with CT and CTE
The longitudinal and transverse helicity fractions in the presence of T operator cou-
plings are plotted in figure 15 Here the response to the different values of T couplings
ndash 25 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 14 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus
on q2 for different values of T-SP couplings The caption for the above figures are the same as
figure 11
are visible both in the high and low q2 regimes The effects are more distinct when CT
coupling is present compared to when only CTE coupling is present When SP couplings
are added along with the T couplings the results are an emulsion of the effects coming from
T as well as high q2 effects of SP (figures 15(bcef))
44 All NP operators together
In presence of all new physics operator couplings of V A S P and T the results as expected
are pretty drastic The combination of all these couplings have most of the attributes of
each individual type of coupling The branching ration plots are shown in figure 16 increases
by a factor of two and depending upon the values of coupling this increase is four times
compared to SM branching ratio (figure 16(b))
The forward backward asymmetry gets scrambled results the zero crossing vanishes
for most values of NP couplings when new bound eq (43) is neglected (figure 17b) If this
new bound is incorporated then the zero position does not vanish but the shift in ZP is
significantly in both directions
The longitudinal lepton polarization varies a lot and takes on both positive and negative
values (figure 18) The normal lepton polarization crosses the zero and become positive for
some values of the NP couplings (figure 19) showing us the presence of SP couplings
ndash 26 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
(d) (e)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
(f)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 15 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of T-SP couplings The caption for the above figures
are the same as figure 11
ndash 27 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
2acute 10-8
4acute 10-8
6acute 10-8
8acute 10-8
1acute 10-7
12acute 10-7
14acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
5acute 10-8
1acute 10-7
15acute 10-7
2acute 10-7
dG qd2H
Breg
K2 H
0341L+Μ++Μ-L
Figure 16 The dependence of decay rate for B0 rarr Klowast
2 (1430)micro+microminus on q2 where different curves
correspond to different choices of the values of all couplings are taken into account inside their
allowed region In all figures the solid line represent the SM with light green shaded region as
uncertainty in SM
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-005
0
005
01
015
02
025
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-01
-005
0
005
01
015
02
AB
FH
Breg
K2 H
0341L+Μ++Μ-L
Figure 17 The dependence of forward-backward asymmetry for B rarr Klowast
2 (1430)micro+microminus on q2 for
different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-05
-025
0
025
05
075
P LH
Breg
K2 H
0341L+Μ++Μ-L
Figure 18 The dependence of Longitudinal lepton polarization asymmetry for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
ndash 28 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
0341L+Μ++Μ-L
Figure 19 The dependence of Normal lepton polarization asymmetry for B rarr Klowast
2 (1430)micro+microminus on
q2 for different values of All couplings The caption for the above figures are the same as figure 16
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
1f LH
Breg
K2 H
0341L+Μ++Μ-L
(c) (d)
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
0
02
04
06
08
f TH
Breg
K2 H
0341L+Μ++Μ-L
Figure 20 The dependence of Longitudinal and Transverse helicity fractions for B rarrKlowast
2 (1430)micro+microminus on q2 for different values of All couplings The caption for the above figures are the
same as figure 16
The longitudinal and transverse helicity fractions are shown in figure 20 for the case
when all couplings are present The deviation from SM values as expected are large since
now all couplings are present
Finally the transverse lepton polarization asymmetry PT acquires non-zero values
when T couplings are present (see eq (319)) In the SM this asymmetry is negligibly small
ndash 29 ndash
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
(a) (b)
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
03P TH
Breg
K2 H
1430L+Μ++Μ-L
0 2 4 6 8 10 12 14q2HGeV2
L
-04
-03
-02
-01
0
01
02
P TH
Breg
K2 H
1430L+Μ++Μ-L
(c)
0 2 4 6 8 10 12 14q2HGeV2
L
-08
-06
-04
-02
0
02
04
P NH
Breg
K2 H
1430L+Μ++Μ-L
Figure 21 The dependence of transverse lepton polarization asymmetry for B0 rarr Klowast
2 (1430)micro+microminus
on q2 where different curves correspond to different choices of the values of all couplings inside their
allowed region and the flat solid line at PT = 0 represent the SM with no uncertainty region In
figure (a) only tensor type couplings are present figures (bc) when all couplings are present
since all Wilson coefficients are predominantly real The transverse lepton polarization
asymmetry will be imaginary if all couplings are real(cf eq (319)) but for imaginary
values of CT CTE couplings it will become a real observable Figure 21 shows PT for
different values of imaginary tensor couplings while all other couplings are taken to be real
It can be seen that for the certain values of NP couplings the value of transverse lepton
polarization is significant It is therefore expected that its experimental observation in
future will help us to get constraints on CT CTE couplings In figure 21a only CT CTE
couplings are present and in figures 21(bc) all other couplings are present too hence the
values of PT become large
5 Conclusions
We carried out the study of the decay B rarr Klowast2 (1430)micro
+microminus in the presence of new physics
(NP) operators beyond SM We have performed a schematic model-independent analysis
allowing for new vector-axial vector (VA) scalar-pseudoscalar (SP) and tensor (T) operator
couplings We analyzed the effects on different physical observables for this channel in
the presence of these NP operator couplings To conclude this study we summarize the
important out comes as follows
ndash 30 ndash
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
bull The differential branching ratios generally increase for most of the parameter space
of NP couplings For V A couplings the BR increases considerably particularly when
both RVA and RprimeVA are involved the BR is enhanced by more than a factor of 4 and
the reason is that the new V A couplings are not ml suppressed compared to other
NP couplings On the other hand the BR for case of SP and T couplings fall mainly
in uncertainty region of SM The reason behind this lies in the fact that SP and T
operator couplings are severely constrained by the upper bound on B(Bs rarr micro+microminus)
as well as their contribution is ml suppressed
bull The forward-backward asymmetry of the final state leptons deviates sizable in the
presence of V A couplings When the new bound given in Eq 43 is ignored the zero
crossing even disappears and its values become all positives or all negative Similar
kind of trend was also witnessed for the decay B rarr Klowast(892)micro+microminus If we consider
the recent measurement of AFB for B rarr Klowast(892)micro+microminus decay at LHCb [15] we
can see that new VA couplings get constrained within a narrow band given in Eq
43 However the new SP couplings contribute delicately to the shifting of the zero
position of AFB for both decays B rarr Klowast(892)micro+microminus [52] and B rarr Klowast2 (1430)micro
+microminus
SP operators couplings particularly S coupling shift the zero crossings both towards
left as well as towards right When T coupling is added to the scene the zero shifting is
enhanced and it even disappears for certain values of SPminusT couplings Qualitatively
the AFB in presence of SP and T couplings separately areml suppressed while SPminusTcouplings together are notml suppressed and hence show large NP effects on the decay
under consideration
bull The longitudinal lepton polarization asymmetry (PL) is also an important tool to
look for physics beyond SM Again the PL is very sensitive V A couplings its values
sway between the positive SM value to negative maximum value for defined range of
RVA and RprimeVA couplings The effects on PL are still mild when S and P couplings
are introduced individually but the effects are magnified when both SP couplings are
present The T couplings also disturb the values of PL and the effects get added up
when both SP and T couplings are in combination
bull The normal lepton polarization asymmetry is not as sensitive to V A operator cou-
plings like the other observables The V A effects on PN are more dominant in the low
q2 region while in high q2 regime they all asymptotically converge to zero The nor-
mal lepton polarization provides an ideal testing ground to test the existence of SP
new physics operators The distinct behavior of PN in the presence of SP couplings
is very important to test the existence of SP as well as SP minus T operators
bull The longitudinal and transverse helicity fraction of the final state meson Klowast2 (1430)
are also efficient tool to look for the NP effects In case of V A operators the there
is a noticeable change in helicity fractions of the final state meson For SP operator
couplings the effects are more prominent in the high q2 regime The tensor couplings
CT and CTE also allow the helicity fractions to deviate significantly from their SM
values
ndash 31 ndash
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
We hope that these results will be tested one some ongoing and future experiments
like LHCb and super B factories
Acknowledgments
The authors greatly acknowledge some helpful discussions with Prof Riazuddin and Prof
Fayyazuddin The authors would also like to thank Ali Paracha for some useful discus-
sions The author JA would like to thank the facilities provided by National Centre for
Physics and also support by Science and Engineering Research Canada (NSERC) during
the revision of this paper
References
[1] BELLE collaboration J-T Wei et al Measurement of the Differential Branching Fraction
and Forward-Backword Asymmetry for B rarr K()ℓ+ℓminus Phys Rev Lett 103 (2009) 171801
[arXiv09040770] [INSPIRE]
[2] BABAR collaboration B Aubert et al Measurements of branching fractions rate
asymmetries and angular distributions in the rare decays B rarr Kℓ+ℓminus and B rarr Klowastℓ+ℓminus
Phys Rev D 73 (2006) 092001 [hep-ex0604007] [INSPIRE]
[3] BABAR collaboration B Aubert et al Angular Distributions in the Decays B rarr K ℓ+ℓminus
Phys Rev D 79 (2009) 031102 [arXiv08044412] [INSPIRE]
[4] E Lunghi and A Soni Hints for the scale of new CP-violating physics from B-CP
anomalies JHEP 08 (2009) 051 [arXiv09035059] [INSPIRE]
[5] Heavy Flavor Averaging Group collaboration E Barberio et al Averages of bminushadronand cminushadron Properties at the End of 2007 arXiv08081297 [INSPIRE]
[6] UTfit collaboration M Bona et al First Evidence of New Physics in blarrrarr s Transitions
PMC Phys A 3 (2009) 6 [arXiv08030659] [INSPIRE]
[7] S Baek C-W Chiang and D London The B rarr pi K Puzzle 2009 Update
Phys Lett B 675 (2009) 59 [arXiv09033086] [INSPIRE]
[8] T Feldmann and J Matias Forward backward and isospin asymmetry for B rarr K ℓ+ℓminus
decay in the standard model and in supersymmetry JHEP 01 (2003) 074 [hep-ph0212158]
[INSPIRE]
[9] BABAR collaboration B Aubert et al Direct CP Lepton Flavor and Isospin Asymmetries
in the Decays B rarr K(lowast)ℓ+ℓminus Phys Rev Lett 102 (2009) 091803 [arXiv08074119]
[INSPIRE]
[10] W Altmannshofer P Ball A Bharucha AJ Buras DM Straub et al Symmetries and
Asymmetries of B rarr Klowastmicro+microminus Decays in the Standard Model and Beyond
JHEP 01 (2009) 019 [arXiv08111214] [INSPIRE]
[11] G Burdman Short distance coefficients and the vanishing of the lepton asymmetry in B rarrV ℓ+ lepton- Phys Rev D 57 (1998) 4254 [hep-ph9710550] [INSPIRE]
[12] A Ali P Ball L Handoko and G Hiller A Comparative study of the decays B rarr (K
Klowast)ℓ+ℓminus in standard model and supersymmetric theories Phys Rev D 61 (2000) 074024
[hep-ph9910221] [INSPIRE]
ndash 32 ndash
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
[13] M Beneke T Feldmann and D Seidel Systematic approach to exclusive B rarr V ℓ+ℓminus V
gamma decays Nucl Phys B 612 (2001) 25 [hep-ph0106067] [INSPIRE]
[14] Belle Finds a Hint of New Physics in Extremely Rare B Decays reported in August 2009 (as
Press Release) httpwwwkekjpintra-epress2009BellePress14ehtml
[15] LHCb collaboration Angular analysis of B0 rarr Klowast0micro+microminus LHCb-CONF-2011-038 (Angular
analysis of B0 rarr Klowast0micro+microminus)
[16] AS Cornell N Gaur and SK Singh FB asymmetries in the B rarr K ℓ+ℓminus decay A Model
independent approach hep-ph0505136 [INSPIRE]
[17] A Ali T Mannel and T Morozumi Forward backward asymmetry of dilepton angular
distribution in the decay b rarr s ℓ+ℓminus Phys Lett B 273 (1991) 505 [INSPIRE]
[18] AJ Buras and M Munz Effective Hamiltonian for B rarr X(s) e+eminus beyond leading
logarithms in the NDR and HV schemes Phys Rev D 52 (1995) 186 [hep-ph9501281]
[INSPIRE]
[19] M Misiak The b rarr s e+eminus and b rarr s gamma decays with next-to-leading logarithmic QCD
corrections Nucl Phys B 393 (1993) 23 [Erratum ibid B 439 (1995) 461] [INSPIRE]
[20] F Kruger and E Lunghi Looking for novel CP-violating effects in B rarr Klowastℓ+ lepton-
Phys Rev D 63 (2001) 014013 [hep-ph0008210] [INSPIRE]
[21] A Ali E Lunghi C Greub and G Hiller Improved model independent analysis of
semileptonic and radiative rare B decays Phys Rev D 66 (2002) 034002 [hep-ph0112300]
[INSPIRE]
[22] A Ghinculov T Hurth G Isidori and Y Yao New NNLL results on the decay B rarr X(s)
ℓ+ℓminus Eur Phys J C 33 (2004) S288 [hep-ph0310187] [INSPIRE]
[23] C Bobeth T Ewerth F Kruger and J Urban Analysis of neutral Higgs boson
contributions to the decays B( s) rarr ℓ+ℓminus and B rarr Kℓ+ℓminus Phys Rev D 64 (2001) 074014
[hep-ph0104284] [INSPIRE]
[24] PH Chankowski and L Slawianowska Effects of the scalar FCNC in brarr sl+ sl- transitions
and supersymmetry Eur Phys J C 33 (2004) 123 [hep-ph0308032] [INSPIRE]
[25] G Hiller and F Kruger More model independent analysis of brarr s processes
Phys Rev D 69 (2004) 074020 [hep-ph0310219] [INSPIRE]
[26] AK Alok and S Sankar New physics upper bound on the branching ratio of Bs rarr ℓ+ℓminus
Phys Lett B 620 (2005) 61 [hep-ph0502120] [INSPIRE]
[27] AK Alok A Dighe and S Sankar Tension between scalarpseudoscalar new physics
contribution to B(s) rarr micro+microminus and B rarr K micro+microminus Mod Phys Lett A 25 (2010) 1099
[arXiv08033511] [INSPIRE]
[28] AK Alok A Dighe and S Sankar Probing extended Higgs sector through rare brarr smicro+microminus
transitions Phys Rev D 78 (2008) 034020 [arXiv08050354] [INSPIRE]
[29] A Hovhannisyan W-S Hou and N Mahajan B rarr K ℓ+ℓminus Forward-backward Asymmetry
and New Physics Phys Rev D 77 (2008) 014016 [hep-ph0701046] [INSPIRE]
[30] F Kruger and J Matias Probing new physics via the transverse amplitudes of B0 rarr K0 (rarrK- pi+) ℓ+ℓminus at large recoil Phys Rev D 71 (2005) 094009 [hep-ph0502060] [INSPIRE]
[31] E Lunghi and J Matias Huge right-handed current effects in B rarr K(K pi)ℓ+ℓminus in
supersymmetry JHEP 04 (2007) 058 [hep-ph0612166] [INSPIRE]
ndash 33 ndash
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
[32] U Egede T Hurth J Matias M Ramon and W Reece New observables in the decay mode
B(d)rarr anti- K0 ℓ+ℓminus JHEP 11 (2008) 032 [arXiv08072589] [INSPIRE]
[33] T Aliev V Bashiry and M Savci Double lepton polarization asymmetries in the B rarr K
ℓ+ℓminus decay beyond the standard model Eur Phys J C 35 (2004) 197 [hep-ph0311294]
[INSPIRE]
[34] T Aliev V Bashiry and M Savci Polarized lepton pair forward backward asymmetries in B
rarr K ℓ+ℓminus decay beyond the standard model JHEP 05 (2004) 037 [hep-ph0403282]
[INSPIRE]
[35] T Aliev M Cakmak A Ozpineci and M Savci New physics effects to the lepton
polarizations in the B rarr K lepton+ lepton- decay Phys Rev D 64 (2001) 055007
[hep-ph0103039] [INSPIRE]
[36] W Bensalem D London N Sinha and R Sinha Lepton polarization and forward backward
asymmetries in b rarr s tau+ tau- Phys Rev D 67 (2003) 034007 [hep-ph0209228]
[INSPIRE]
[37] AK Alok A Dighe D Ghosh D London J Matias et al New-physics contributions to
the forward-backward asymmetry in B rarr K micro+microminus JHEP 02 (2010) 053
[arXiv09121382] [INSPIRE]
[38] W Wang B to tensor meson form factors in the perturbative QCD approach
Phys Rev D 83 (2011) 014008 [arXiv10085326] [INSPIRE]
[39] K-C Yang B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules
Phys Lett B 695 (2011) 444 [arXiv10102944] [INSPIRE]
[40] R-H Li C-D Lu and W Wang Branching ratios forward-backward asymmetries and
angular distributions of B rarr Klowast
2 l+lminus in the standard model and new physics scenarios
Phys Rev D 83 (2011) 034034 [arXiv10122129] [INSPIRE]
[41] N Katirci and K Azizi B to strange tensor meson transition in a model with one universal
extra dimension JHEP 07 (2011) 043 [arXiv11053636] [INSPIRE]
[42] H Hatanaka and K-C Yang Radiative and Semileptonic B Decays Involving the Tensor
Meson K(2)(1430) in the Standard Model and Beyond Phys Rev D 79 (2009) 114008
[arXiv09031917] [INSPIRE]
[43] S Choudhury A Cornell and N Gaur Analysis of the B rarr K(2)(1430)ℓ+ℓminus decay
Phys Rev D 81 (2010) 094018 [arXiv09114783] [INSPIRE]
[44] S Choudhury A Cornell and J Roussos Analysis of the lepton polarisation asymmetries of
B rarr K2(1430) ℓ+ ℓminus decay Eur Phys J C 71 (2011) 1751 [arXiv11055901] [INSPIRE]
[45] M Junaid and M Aslam Complementarity of Semileptonic B to Klowast
2 (1430) and Klowast(892)
Decays in the Standard Model with Fourth Generation arXiv11033934 [INSPIRE]
[46] T Aliev and M Savci B rarr K2ℓ+ℓminus decay beyond the Standard Model
Phys Rev D 85 (2012) 015007 [arXiv11092738] 18 pages 5 figures LaTeX formatted
[INSPIRE]
[47] CDF collaboration T Aaltonen et al Search for B0s rarr micro+microminus and B0
d rarr micro+microminus decays with
2fbminus1 of pp collisions Phys Rev Lett 100 (2008) 101802 [arXiv07121708] [INSPIRE]
[48] Particle Data Group C Amsler et al Review of Particle Physics
Phys Lett B 667 (2008) 1
ndash 34 ndash
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-
JHEP02(2012)045
[49] BABAR collaboration B Aubert et al Measurement of the B rarr Xsℓ+ℓminus branching
fraction with a sum over exclusive modes Phys Rev Lett 93 (2004) 081802
[hep-ex0404006] [INSPIRE]
[50] Belle collaboration M Iwasaki et al Improved measurement of the electroweak penguin
process B rarr X(s) ℓ+ℓminus Phys Rev D 72 (2005) 092005 [hep-ex0503044] [INSPIRE]
[51] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Conserving Observables JHEP 11 (2011) 121 [arXiv10082367] [INSPIRE]
[52] AK Alok A Datta A Dighe M Duraisamy D Ghosh et al New Physics in b rarr s
micro+microminus CP-Violating Observables JHEP 11 (2011) 122 [arXiv11035344] [INSPIRE]
[53] J-P Lee Radiative B decays to the axial K mesons at next-to-leading order
Phys Rev D 69 (2004) 114007 [hep-ph0403034] 17pages 4 figures Minor changes typos
corrected PRD accepted version [INSPIRE]
[54] M Beneke Hadronic B decays with QCD factorization Int J Mod Phys A 21 (2006) 642
[hep-ph0509297] [INSPIRE]
[55] TM Aliev and M Savci Λb rarr Λl+lminus decay in Universal Extra Dimensions
Eur Phys J C 50 (2007) 91 [hep-ph0606225] [INSPIRE]
[56] Particle Data Group collaboration K Nakamura et al Review of particle physics
J Phys G 37 (2010) 075021 [INSPIRE]
ndash 35 ndash
- Introduction
- B -gt K(2) (1430) mu+ mu- operators and matrix elements
-
- Standard model
- New physics operators
- Parametrization of matrix elements and form factors
- Numerical constraints on NP parameters
-
- Decay rate forward-backward asymmetry and lepton polarization asymmetries for B-gt K(2) (1430) mu+ mu- decay
-
- Differential decay rate
- Forward-backward asymmetry
- Lepton polarization asymmetries
- Helicity fractions
-
- Numerical Analysis
-
- VA new-physics operators
- SP new-physics operators
- T operators and interference of SP and T operators
- All NP operators together
-
- Conclusions
-