Post on 21-Dec-2015
Testing the SM with penguin-dominated B-decays
Amarjit Soni
HET,BNL
(soni@bnl.gov)
Outline• How good a null test is this? • How well does the penguin-dominate?• Possible dynamical enhancement of u-quark ?• Why (LD)FSI has become a significant concern?• How can we tackle this complication?• How well can we exploit correlation between
ΔSf (=Sf – SψK ) and Cf ?• Can we make stronger statement about the sign of ΔSf ?
• Are there (theoretically) problematic modes?• Averaging issue• Summary and Conclusions
.
Questions for the Super-B Workshop
Brief Recapitulation: Basic Idea
Dominant decay amp.has0 weak phase [just as in
B->ψKS] up to O(λ2)
Brief remarks on the old study(with London, PLB’97)
• Originally motivated by the thenCLEO discovery of• Huge inclusive (see Browder..) as well as exclusive• (see J. Smith…) Brs. into η’ • Suggest with Atwood(PLB97;PRL97) use of η’ Xs(d)
• for search of NP via DIRCP as in SM expect very small• With London suggest use of MICP in [η’ ,
η ,π0,ρ0,ω,φ….]KS to test CKM-paradigm via sin2φ1(β)• Present simple (naïve) estimates of T/P …for• All cases T/P <0.04• Due to obvious limitations of method suggest conservative• Bound ΔSf <0.10 for the SM
For DIRCP see also Hou&Tseng,PRL’98
J. Smith@CKM05
WA ~ 2.7σ
Physics Summary SBF'05 HawaiiJ.Smith@CKM05
Averaging issue:Are we makinga mountain outa anthill?
• I am rather sceptical and concerned about
averaging over many small deviations,
leading to ~3.7 σ ….On the other hand,
London&A.S,hep-ph/9704277
Null Test(s)• In light of B-factory results (existing exptal
info+lattice+phenomenology)-> deviations from CKM-paradigm due BSM-CP-odd phase(s) are likely to be small-> should develop Null Tests
• Since CP is not an exact symmetry of SM->No EXACT NULL TESTS-> Need “Approximate Null Tests” (ANTs).
• In b->s transitions, penguin-dominated B-decays are a powerful ANT• W(“worthiness”)=C(“cleanliness”) X S(“sensitivity”)=4.5* X 5*• ANT: In large class of modes such as (π0,ρ,ω,η’,φ,f0,K0K0…)K0 ,
(penguin/Total) ~ 1 -> ΔSf ~0• Summary of early (London + AS, PLB’97) study….• ΔSf < 0.1 in the SM (for modes discussed therein)• Summary of Recent Reaxmination (Cheng,Chua+AS,hepph/0502235….) ,
ΔSf > 0.1 most likely due BSM-CP-odd phase (for many modes)
Browder&A.S,hep-ph/04 10192
A possible complications: large FSI phases in 2-body B decays
• The original papers predicting ΔSf=Sf - SψK ~0 used naïve factorization ideas; in particular FSI were completely ignored.A remarkable discovery of the past year is that directCP in charmless 2-body modes is very large->(LD)FS phases in B-decays need not be smallSINCE THESE ARE INHERENTLYNon-perturbative model dependence becomesunavoidable
3
F S I i n c h a r m l e s s B d e c a y s F S I i n c h a r m l e s s B d e c a y s
723 10.3 6.5 2437
7.1 9.12 0.6 48
517 4.1 4.5 211
2.131.00.31.28.123.08.21.2
0
1.02.0
5.111.03.12.07.111.06.11.0
1415
0
7.85.02.21.15.96.05.21.1
0
B
B
KB
E x p t ( % ) Q C D F ( B N ) Q C D F ( S 4 ) p Q C D
1 . D i r e c t C P v i o l a t i o n
p Q C D ( K e u m , L i , S a n d a ) : A s i z a b l e s t r o n g p h a s e f r o m p e n g u i n -i n d u c e d a n n i h i l a t i o n b y i n t r o d u c i n g p a r t o n ’ s t r a n s v e r s e m o m e n t u m
Q C D F ( S 4 ) s c e n a r i o : l a r g e a n n i h i l a t i o n w i t h p h a s e c h o s e n s o t h a t a c o r r e c t s i g n o f A ( K + - ) i s p r o d u c e d ( A = 1 , A = - 5 5 f o r P P )
I t i s c o n c e i v a b l e t h a t L D s t r o n g p h a s e s i n d u c e d f r o m F S I sw i l l h a v e a s t r o n g i m p a c t o n D C P V p h e n o m e n o l o g y
D C P V s i n s i n ( : w e a k p h a s e , : s t r o n g p h a s e )
HYC-CKM05
4
2. Some color-suppressed or factorization-forbidden or penguin-dominated modes cannot be accommodated in the naïve factorization approach
Some decay modes do not receive factorizable contributions
e.g. B K0c with sizable BR though 0c|c(1-5)c|0=0.
Color-suppressed modes e.g. B0 D0 h0 (h0=0,,0,,’), 00, 00
have the measured rates larger than theoretical expectations.
Penguin-dominated modes such as B K*, K, K, K* predicted by QCDF are consistently lower than experiment by a factor of 2 3
importance of power corrections (inverse powers of mb)e.g. FSI, annihilation, EW penguin, New Physics, …
HYC-CKM05
5
Regge approach [Donoghue,Golowich,Petrov,Soares]
FSI phase is dominated by inelastic scattering and doesn’t vanish even
in mb limit
QCDF [Beneke,Buchalla,Neubert,Sachrajda]
strong phase is O(s, /mb): systematic cancellation of FSIs in mb
Charming penguin [Ciuchini et al.] [Colangelo et al.] [Isola et al.]
long distance in nature, sources of strong phases, supported by SCET
One-particle-exchange model for LD rescatteringhas been applied to charm and B decays [Lu,Zou,..], [Du et al.]
Quasi elastic scattering model [Chua,Hou,Yang]
Consider MM MM (M: octet meson) rescattering in B PP decays
Diagrammatic approach [Chiang et al.] …
Approaches for FSIs in charmless B decays
HYC-CKM05
7
F S I a s r e s c a t t e r i n g o f i n t e r m e d i a t e t w o - b o d y s t a t e s
[ H Y C , C h u a , S o n i ]
F S I s v i a r e s o n a n c e s a r e a s s u m e d t o b e s u p p r e s s e d i n B d e c a y s d u e t o t h e l a c k o f r e s o n a n c e s a t e n e r g i e s c l o s e t o B m a s s .
F S I i s a s s u m e d t o b e d o m i n a t e d b y r e s c a t t e r i n g o f t w o - b o d y i n t e r m e d i a t e s t a t e s w i t h o n e p a r t i c l e e x c h a n g e i n t - c h a n n e l . I t s a b s o r p t i v e p a r t i s c o m p u t e d v i a o p t i c a l t h e o r e m :
i
ifTiBMfBMm )()( 2
• S t r o n g c o u p l i n g i s f i x e d o n s h e l l . F o r i n t e r m e d i a t e h e a v y m e s o n s ,
a p p l y H Q E T + C h P T ( f o r s o f t G o l d s t o n e b o s o n )
• F o r m f a c t o r o r c u t o f f m u s t b e i n t r o d u c e d a s e x c h a n g e d p a r t i c l e i s
o f f - s h e l l a n d f i n a l s t a t e s a r e h a r d
A l t e r n a t i v e : R e g g e t r a j e c t o r y [ N a r d u l l i , P h a m ] [ F a l k e t a l . ] [ D u e t a l . ] …
8
D i s p e r s i v e p a r t i s o b t a i n e d f r o m t h e a b s o r p t i v e a m p l i t u d e v i a d i s p e r s i o n r e l a t i o n
''
)'( )(
0
22 ds
ms
sMmPmMe
s BB
= m e x c + r Q C D ( r : o f o r d e r u n i t y )
o r r i s d e t e r m i n e d f o r m a 2 f i t t o t h e m e a s u r e d r a t e s
r i s p r o c e s s d e p e n d e n t
n = 1 ( m o n o p o l e b e h a v i o r ) , c o n s i s t e n t w i t h Q C D s u m r u l e s
O n c e c u t o f f i s f i x e d C P V c a n b e p r e d i c t e d
s u b j e c t t o l a r g e u n c e r t a i n t i e s a n d w i l l b e i g n o r e d i n t h e p r e s e n t w o r k
F o r m f a c t o r i s i n t r o d u c e d t o r e n d e r p e r t u r b a t i v e c a l c u l a t i o n m e a n i n g f u l
n
QCD
n
t
m
t
mtF
2
22
)(
L D a m p . v a n i s h e s i n H Q l i m i t
All rescattering diagrams contribute to penguin topology,
dominated by charm intermediate states
fit to rates rD = rD* 0.67
predict direct CPV
B B
Should reduce model dependence Significantly for CPV
1 8
T h e o r e t i c a l u n c e r t a i n t i e s
1 . M o d e l a s s u m p t i o n
- - m u l t i - b o d y c o n t r i b u t i o n s
- - f o r m - f a c t o r c u t o f f :
i ) . n = 1
i i ) . = m e x c + r Q C D (1 5 % e r r o r a s s ig n e d fo r Q C D )
r D = 2 .1 , 1 .6 , 0 .7 3 , 0 .6 7 , r e s p e c tiv e ly , fo r D , , K m o d e s
0 .9 5 fo r p e n g u in -d o m in a te d P V m o d e s
- - d i s p e r s i v e c o n t r i b u t i o n
2 . I n p u t p a r a m e t e r s
- - s t r o n g c o u p l i n g s o f h e a v y m e s o n s a n d t h e i r S U ( 3 ) b r e a k i n g
- - f o r m f a c t o r s & d e c a y c o n s t a n t s
- - s t r a n g e q u a r k m a s s
n
t
mtF
2
22
)(
22
FSI effect is tiny due to small source (K*,K) amplitudes (Br~10-6) compared to Ds*D (Br~10-2,-3). It tends to alleviate the deviation from sin2
DCPV is predicted to be of order 15% in KS, 50% in 0KS and a few percents in all other modes.
---0.50+0.06-0.02-0.11--0.722+0.066
-0.0720.6240KS
?
0.7740.008
0.7320.001
0.7360.016
0.7550.006
SD+LD
?
-0.0240.009
-0.0210.0
0.1510.018
0.025+0.002-0.005
SD+LD
0.140.22-0.0080.390.260.747f0KS
0.090.140.0430.340.280.7820KS
-0.040.08-0.0180.410.110.735‘KS
-0.490.250.0760.560.320.850KS
-0.040.17-0.0170.340.200.745KS
ExptSDExptSD
Cf-nfSf
HYC-CKM05
Cheng,Chua,A.S.Hep-ph/0502235
1.Note in SD, ΔS switches sign bet. ω,ρ for us no change2. LD rescattering effects on S & C are highly correlated and similarlyC’s of isospin partners are correlated -> many testable predictions,e.g
LARGE (13%)DIR CP for ω KS & HUGE for ρ KS (~ -46%)
Correlation between MixingInduced and Direct CP
BR
SD
(10-6)
BR
with FSI
(10-6)
BR
Expt
(10-6)
DCPV
SD
DCPV
with FSI
DCPV
Expt
B 16.6 22.9+4.9-3.1 24.11.3 0.01 0.026+0.00
-0.002 -0.020.03
B0 13.7 19.7+4.6-2.9 18.20.8 0.03 -0.15+0.03
-0.01 -0.110.02
B0 9.3 12.1+2.4-1.5 12.10.8 0.17 -0.09+0.06
-0.04 0.040.04
B0 6.0 9.0+2.3-1.5
11.51.0 -0.04 0.022+0.008-0.012 -0.090.14
Only LD uncertainties due to form-factor cutoff are shown here.
Total errors=SD+LD, for example,
FSI yields correct sign and magnitude for A(+K-)
P/T|SD=0.12 exp(-i177), P/TSD+LD=(0.140.01)exp[i(1478)]
_
_
_
_
)(7.19)(7.13)(10 6.45.109.23.5
6.105.5
06 LDSDSDKBBr
17
--0.50+0.06-0.020.105.11.65.0+1.3
-0.82.9B0
---0.40+0.02-0.08-0.0135.15+0.91
-0.893.9+1.5-0.91.2B 0
0.17+0.15-0.16-0.18+0.04
-0.060.0329.9+1.6-1.511.1+2.9
-1.94.2B0 +
---0.008+0.001-0.0020.004 <489.8+3.0
-1.93.1B
DCPV
Expt
DCPV
with FSI
DCPV
SD
BR
Expt
(10-6)
BR
with FSI
(10-6)
BR
SD
(10-6)
B B
_
_
PV/TV|SD=0.040 exp(-i3 ),
PV/TV|SD+LD=(0.079+0.012
-0.009) exp[i(2710) ]
|P/T|SD is smaller than K* case due to opposite sign between a4 and a6
_
_
Note the very large (~ -40%) DCP in ρ0 K- & ρ0 K0
More remarks
& ρ0KS May be a goodway
Based on our study it seems difficult to accommodateΔS>0.10 within the SM at least for KS[ή,φ]
Summary (1 of 2)1) Penguin dominated B-decays (b->s) are very useful “ANTs” of SM;
for many modes ΔS>0.10 difficult to accommodate in SM.
2) The η’ KS is esp. clean…due dominance of Penguin (huge Br), which
was in fact the original motivation for suggesting the η’ ; Model calculations show ΔS(η’ KS )~0.01. Since expt. Error for η’ KS
is smallest (0.11), prospects for precision for this mode seem promising.
3) S-C correlation provides a very useful check On the models -> improved expt. measurements should lead to improvements in the models -> other modes may also become useful.
4) Noteable predictions of our model: large dir.CP in [ π,ρ] K- , [ρ,ω]KS
5) The sign of ΔS in our (and several other) model(s) tends to be positive
with small central value (compared to largish ) errors; thus conclusive
statements regarding the sign are difficult to make (Exptal. sign of ΔS
tends to be negative!)
Sign of ΔS in the SMMode pQCD(SM ) QCDF(MB) QCDF+FSI(CCS)
η’KS .01(.01,-.01) .00(.00,-.04)
φKS ..020(.004,-.008) .02(.01,-.01) .03(.01,-.04)
πKS .009(.001,-.003) .07(.05,-.04) .04(.02,-.03)
Summary (2):Bottomline
Most of the effect currently is driven by
the largish ΔS for η’ KS . If New Physics is responsible for this then NP MUST show up in numerous (b ->s) channels e.g. η’ K- , φ[K0,K-…](*), affecting mixing,
dir and triple-corr CP…AND BS physics. Also, in all liklihood, radiative , leptonic (b->s) should also be effected making Expts. With higher luminosities extremely rich and exciting!