2006-2-24Bc meson physics1 Chao-Hsi Chang ( 张肇西 ) I.T.P., Chinese Academy of Sciences 1. The...
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Transcript of 2006-2-24Bc meson physics1 Chao-Hsi Chang ( 张肇西 ) I.T.P., Chinese Academy of Sciences 1. The...
2006-2-24 Bc meson physics 1
Chao-Hsi Chang ( 张肇西 ) I.T.P., Chinese Academy of Sciences
1. The meson Bc2. Mass, lifetime & decays3. Production (theoretical estimates) a. Production at Z0 (at LEP-I) b. Hadronic Production (at Tevatron & LHC)4. Experimental status 5. Prospect for LHC6. Comment on Ji’s paper
Bc Meson Physics
2006-2-24 Bc meson physics 2
1. The meson Bc
Of the six quarks u c t u c t d s b
- u, d, s, light - c, b, t , heavy (top lifetime τ too short to form hadrons)
Bc: double heavy explicit-flavored meson (unique)
Experimental studies are at the stage: 1998-discovery, 2005 new results, ……
2006-2-24 Bc meson physics 3
2. Mass, lifetime & decays
Bc mass: according to PM & Lattice QCD
Bc lifetime: Weak decay only (no strong &EM decay) According to spectator model and B & D mesons’ lifetime: we may obtain (the earliest 1994: PRD 49 3399)
More careful estimate
in vertex detector ability
2006-2-24 Bc meson physics 4
2. Mass, lifetime & decays
:
:
Phys. Rev. D. 64, 014003, 2001
: :
2006-2-24 Bc meson physics 5
2. Mass, lifetime & decays
Bc decays: weak decays (Mandelstam formulation & instantaneous BS equation)
2006-2-24 Bc meson physics 6
2. Mass, lifetime & decays
Mandelstam formulation (Composite quantum field theory) Transitions (decays with great momentum recoil)
2006-2-24 Bc meson physics 7
2. Mass, lifetime & decays
2006-2-24 Bc meson physics 8
2. Mass, lifetime & decays
2006-2-24 Bc meson physics 9
2. Mass, lifetime & decays
2006-2-24 Bc meson physics 10
2. Mass, lifetime & decays
The results for various decays• Pure leptonic (radiative) decays :
The radiative decays escaped from chiral suppression !
2006-2-24 Bc meson physics 11
2. Mass, lifetime & decays
• Semileptonic decays (S-wave product):
One I-W function
2006-2-24 Bc meson physics 12
2. Mass, lifetime & decays
• Semileptonic decays (P-wave product or ):
Two I-W functions
Recoil one
Normal one
Spectrum of charged lepton in the decays:
2006-2-24 Bc meson physics 13
2. Mass, lifetime & decays
• Nonleptonic decays (S-wave product):
2006-2-24 Bc meson physics 14
2. Mass, lifetime & decays• Nonleptonic decays (P-wave product or ):
2006-2-24 Bc meson physics 15
2. Mass, lifetime & decays
• The lifetime is quite long that the vertices of production and decay can be detected by vertex detector experimentally (in the window).• Sizable decay channels are rich.• The branch ratio of the decay to is quite great.• The branch ratio of decay to or is large.• Radiative pure leptonic decays escape from chiral suppression. • …….
2006-2-24 Bc meson physics 16
3. Production (theoretical estimates)
It had not expected the difficulty of Bc production
before our prediction for such `light meson’ Bc
(LUND model is not applicable):
The reliable theoretical prediction (most favorable
mechanism):• At Z0 (LEP-I) Bc can be produced marginally.• Only at very high energy hadronic colliders
(Tevatron and LHC) numerous Bc mesons can be
produced for experimental studies.
2006-2-24 Bc meson physics 17
3a. Production at Z0 (at LEP-I)
We explicitly pointed out LUND model
is not applicable and the mechanism
should be as the left figure.
The key point is the hard gluon & it can
be QCD factorized as indicated by the
figure. PRD46, (1992) 3845; PLB284,(1992) 127;……
微扰因子
+ …硬胶子
Z0
The result is that at Z0 peak for LEP-I several thousands of Bc may be produced per year ! Considering the detecting efficiency, to observe Bc at LEP-I is on the margin.
2006-2-24 Bc meson physics 18
3b. Hadronic Production at Tevatron & LHC
Gluon-gluon fusion mechanism dominant
36 Feynman diagrams for complete calculations
The information about the accompany quark-jets interests experimentalists
QCD factorization:
Subprocess:
硬胶子
微扰因子
2006-2-24 Bc meson physics 19
3b. Hadronic Production at Tevatron & LHC
The lowest order calculations: uncertainties from
2006-2-24 Bc meson physics 20
3b. Hadronic Production at Tevatron & LHC
Tevatron
LHC
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3b. Hadronic Production at Tevatron & LHC
and
2006-2-24 Bc meson physics 22
3b. Hadronic Production at Tevatron & LHC
Uncertainties: quite great; sensitive to Q2, mc
high order calculation can suppress them but too complicated.
2006-2-24 Bc meson physics 23
3b. Hadronic Production at Tevatron & LHCP-wave excited state production
To match the wave functions correctly (special attention on the spin structure), we start with the Mandelstam formulation on BS solution:
2006-2-24 Bc meson physics 24
3b. Hadronic Production at Tevatron & LHC
1P1
3P1 3P23P0
3P0
3P1
1P1
3P2
LHC TEVATRON
2006-2-24 Bc meson physics 25
3b. Hadronic Production at Tevatron & LHC
Color octet may be comparable with that of color singlet
Color-singlet (P-wave):
Color-octet (S-wave):
2006-2-24 Bc meson physics 26
3b. Hadronic Production at Tevatron & LHC
LHC
Tevatron
2006-2-24 Bc meson physics 27
3b. Hadronic Production at Tevatron & LHC
Color octet may be comparable with that of color singlet
Color-singlet (P-wave):
Color-octet (S-wave):
2006-2-24 Bc meson physics 28
3b. Hadronic Production at Tevatron & LHC
Intrinsic charm & bottom mechanisms:
Intrinsic charm mechanism (general-mass variable-flavor-number GM-VFN scheme):
Gluon-gluon fusion mechanism (in fixed flavor number FFN scheme and in GM-VFN scheme):
There is a ‘double counting’ (in GM-VFN scheme) due to structure functions, so one must deduct it when summing up the contributions
from the two mechanisms.
2006-2-24 Bc meson physics 29
3b. Hadronic Production at Tevatron & LHC
2006-2-24 Bc meson physics 30
3b. Hadronic Production at Tevatron & LHC
LHC:
Tevatron:
2006-2-24 Bc meson physics 31
3b. Hadronic Production at Tevatron & LHC
LHC:
Tevatron:
FFN gg-fusion
GM-VFN intrinsic + gg-fusion
Intrinsic charm and bottom in GM-VFN scheme makes difference from general FFN scheme only at very small Pt region.
2006-2-24 Bc meson physics 32
• The cross section of Bc at LHC is greater than that at Tevatron by one or two order of magnitude• The uncertainties are quite big at LO QCD• The cross section is at the order 10-3 of B meson production
3b. Hadronic Production at Tevatron & LHC
Experimental needs of the M.C. generator:Difficulties of the experiments in Hadronic ColliderHigh efficiency for the generator
Generator: BCVEGPY1.0 (S-wave, helicity techniques )
BCVEGPY2.0 (S,P-wave, Color-octet,…)
Signals for feasibility studies
CPC Lib. & hppt://www.itp.ac.cn/~zhangzx/
2006-2-24 Bc meson physics 33
4. Experimental status
We predicted LEP-I may and may not observe
Bc meson.
LEP-I (at Z0 peak): ALAPH
DELPHI
OPAL
tried to observe Bc seriously
The result:
Cannot conclude: `discovery of Bc meson’ due to small `statistics’
but it consists with the prediction !
2006-2-24 Bc meson physics 34
Main Injector(new)
Tevatron
DØCDF
Chicago
p source
Booster
Discovery of Bc meson (CDF at Tevatron)
2006-2-24 Bc meson physics 35
- 110 Pb-1 data PRD 58 (1998) 112004
- The only previous evidence by CDF RunI
-- Br~2.4% + trilepton final state + easy to trigger
Bc± J/(+-) ±
CDF discovery (1998 Observation)
2006-2-24 Bc meson physics 36
Experimental progress (D0 result)
D0 result (Observation I New, 2004)Events
Selection: - 210pb-1 data - di-muon triggered- M(+-) within 0.25 GeV of J/- a third track (pT>1.5) with best common vertex fit to J/() : “J/+1 track” data control sample- The third “+1” track should be muon, with M(J/) < 8 GeV After Selection:
due to missing neutrals, the select samples are polluted by background severely use () invariant mass and pseudo proper time distributions to fit
ICHEP'04 & Fermilab 4539-conf
2006-2-24 Bc meson physics 37
Experimental progress (D0 result)
Background shape (data):
- Divided into 2 subsets: 1) “prompt” J/ ( T<0) 2) “heavy flavor” from B (T>0)- Cross-checked with(2S) + 1 track bkg dominated data- Use J/+1 track control data sample
Signal shape (MC):
- MC templates of MBc 5.5 – 6.7 with 0.1GeV interval- Full detector smearing + Selection
Bc Fit: Extract signal from a combined unbinned likelihood fit to J/invariant mass and proper time
5.95 ±0.34 GeV+0.14
-0.13
Bc mass log likelihood
2006-2-24 Bc meson physics 38
Experimental progress (D0 result)“Floating” fit signal + bkg distributions:
Signal 95.5±11.8
Total 231
Prompt 66.0
Heavy F 69.5
Number of events
With significance SB in excess of
5 standard deviations
2006-2-24 Bc meson physics 39
Experimental progress (D0 result)
Consistency check:Simple counting
analysis- normalize background J/+1 track sample to selected sample with T>2
- check excess consistency with data
Fit w/o signal
2log(likelihood)=60 for 5 degrees of freedom
2006-2-24 Bc meson physics 40
Experimental progress (D0 result)
D0 results:
-Preliminary results on Bc with significantly more statistics
Mass: 5.95 ±0.34 GeV/c2 +0.14
-0.13
Events: 95 ± 12±11 in some 200pb-1
Lifetime: 0.448 ±0.121 ps +0.123
-0.096
2006-2-24 Bc meson physics 41
Experimental progress (CDF result)
CDF result (Observation II New, 2005) hep-ex/0505076
The observation II of
Bc J/(+-) +
Exclusive process (mass measurement)
Theor. Refs.: BCVEGPY CPC 159 192, (2004)
Uncertainties Eur. Phys. J. C. 38 267, (2004)
Special Acknowledgement (to us)
2006-2-24 Bc meson physics 42
360 pb from the `` '' -trigger stream
The significance function (score function )
S = Monte Carlo signal B = measured background
The control sample (important):
Experimental progress (CDF result)
2006-2-24 Bc meson physics 43
Experimental progress (CDF result)
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Experimental progress (CDF result)
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vs
(m-100MeV~m+200MeV)
Experimental progress (CDF result)
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Experimental progress (CDF result)
The mass of Bc (mBc)
2006-2-24 Bc meson physics 47
Experimental progress (CDF result)
Summary (CDF RUN-II, ECM=1.96 TeV, 360pb-1)
18.9±5.7 events
mBc=6285.7±5.3(stat)±1.2(syst) MeV/c2
New Result (version 2)
2006-2-24 Bc meson physics 48
5. Prospect for LHCbi). Repeat Tevatron results (mass, lifetime etc) P+P → Bc+… Bc → J/ψ+ l++ν J/ψ+ π (ρ) ii). New decay chennals (relative branching ratios) P+P → Bc+…
Bc → χC (hC) + l++ν
χC (hC) + π(ρ)
Bs (Bs *)+ l++ν Bs (Bs *) + π(ρ) etc
2006-2-24 Bc meson physics 49
5. Prospect for LHC
iii). Deeper studies (with profound understanding the beam and your detector)
Precise measurements of the production: The mechanisms (NRQCD) Excited Bc (P-wave) production etc. (potential model) Form factor measurements in semileptonic decays etc Study of the ‘self-tag’ of Bs ( for mixing) Bc → Bs (Bs *)+ l++ν
Bs (Bs *) + π(ρ, a1) etc Something else Bc → light hadrons+ l++ν (color octet in Bc)
2006-2-24 Bc meson physics 50
About the source for tagged Bs
- Bc Bs + h+ + X?
beam beam※PV
Bc: 140m
6.4GeV?
Bs: 438m
5.4GeV Oscilla.
h+: , ,,e() tracks: pT~100-500MeV,too soft, off-line only
※Ds- : 147m
1.968GeV
※K
0*
-
K+
K-
(36%)
(8%)
(3.3%)
(100%)
- associated h+ + Bs() Bc tag, e.g. open angle, invariant mass in Bc window, common vertex? Br ~ 36%×8%×3.3%×100% ~ 1×10-3
- Br[ BcBs +h+ +X ] or/and Bs CP violation source? motivation and detail crucial to Bc decay vertex, namely no in Bs decay
2006-2-24 Bc meson physics 51
About the source for tagged Bs
beam beam
-
※PV
Bc: 140m
6.4GeV
Bs: 438m
5.4GeV
oscillati
on
h+: , ,,e() tracks: pT~100-500MeV,too soft, off-line only
※Ds- : 147m
1.968GeV
※K
0*
K+
K-
(36%)
(13%)
(3.3%)
(100%)
※
b-jet(B0,B+)
(pT>1) Br~10%!- Bs decay: the Bc decay vertex might be fixed with soft h+ tracks, Br increases by 50%
- without in Bc/Bs chain, how to trigger? from the other side b-quark fragmentation Muon + opposite 2ndVTX (on Ds)
2006-2-24 Bc meson physics 52
About the source for tagged Bs
Potential BcBs+h++X Branching ratio and
Bs CP measurement cross-check ~ O(103) Need investigation !
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向 C. Rubbia 说明 Bc 介子产生的困难 , 需要 LHC( 1992 )
2006-2-24 Bc meson physics 54
6. Comment on Ji’s paper 文章 PRD35(1987)3318 作者 C.R. Ji 等没有认识‘可计算
性’的要领 : 1. 虽然计算了相同的费曼图(右图),但是论文自 始至终没有正确地说明其中的胶子一定是‘硬’的。 2. 相反将理论计算结果应用到未必一定是‘硬’的情 况 B, D ,… 介子等(例如: Figs.2, 3, 4, 5, 6, 7 和相 关的文字)。如果是上述胶子产生的夸克是轻夸 克 u, d, s 等时,则当这些轻夸克的动量很小和 / 或与产生出来的介子动量非常
平行时,上述胶子可以是‘软’的;进入到了微扰 QCD 不能应用的非微扰区,这时的计算变得适用。(重要的差别是重夸克质量大,保证了在胶子‘硬’)
3. 作者没有抓住问题可计算性的关键的证明还有:他们不从‘新产生’的夸克对来考察上述胶子的‘硬’和‘软’;相反他们专门写了附录,企图从另外一个夸克来考察胶子的‘硬’和‘软’,‘误导’读者!
+ ……
2006-2-24 Bc meson physics 55
‘ 最早计算出碎裂函数’和 Bc 产生的计算方法
• C.R. Ji 等的文章 PRD35(1987)3318 在计算碎裂函数时丢了项,而不是所谓的‘低级近似’ :
这点在我们的论文 PRD46(1992)3845 中有明确论证如下:
+ …
为了表明在此产生一对重夸克,用折点表示。
计算碎裂函数时(对应左图),首先得到:
左式( 9 , 10 )中的
a1, a2 是‘常量’ , d 是小量。式( 9 )是按 d 的展开的。其中 z 的运动学限:
2006-2-24 Bc meson physics 56
‘ 最早计算出碎裂函数’和产生的计算方法
对 z 积分(上下限分别为 z1, z2 ) , 得:
韩国人 Ji 的论文 [ 见前页公式( 9 ) ] ,把正比 W1(p), W2
(p) 的项(所谓 d 的高阶项)略去了,因
此,他们最后结果中不包含正比 F1(p), F2
(p) 项,即丢了项,没有得到正确结果。不能说他们的最后结果是‘低阶近似’!
左中的 F0(p), F1
(p), F2(p) 是前面式子
中,对应正比 W0(p), W1
(p), W2(p) 的项
积分得来的。从左结果公式( 12 ,13 )明显可以看出对于 d 而言
F0(p), F1
(p), F2(p)
是同一阶的。表明相空间积分会有实质贡献。
2006-2-24 Bc meson physics 57
Thanks