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


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, ……


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



:

:

Phys. Rev. D. 64, 014003, 2001

: :



Bc decays: weak decays (Mandelstam formulation & instantaneous BS equation)



Mandelstam formulation (Composite quantum field theory) Transitions (decays with great momentum recoil)



The results for various decays• Pure leptonic (radiative) decays :

The radiative decays escaped from chiral suppression !



• Semileptonic decays (S-wave product):

One I-W function



• Semileptonic decays (P-wave product or ):

Two I-W functions

Recoil one

Normal one

Spectrum of charged lepton in the decays:



• Nonleptonic decays (S-wave product):


2. Mass, lifetime & decays• Nonleptonic decays (P-wave product or ):



• 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. • …….


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.


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.


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



The lowest order calculations: uncertainties from



Tevatron

LHC



and



Uncertainties: quite great; sensitive to Q2, mc

high order calculation can suppress them but too complicated.


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:



1P1

3P1 3P23P0

3P0

3P1

1P1

3P2

LHC TEVATRON



Color octet may be comparable with that of color singlet

Color-singlet (P-wave):

Color-octet (S-wave):



LHC

Tevatron



Color octet may be comparable with that of color singlet

Color-singlet (P-wave):

Color-octet (S-wave):



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.



LHC:

Tevatron:



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.


• 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


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/


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 !


Main Injector(new)

Tevatron

DØCDF

Chicago

p source

Booster

Discovery of Bc meson (CDF at Tevatron)


- 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)


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



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


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



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



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


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)


360 pb from the `` '' -trigger stream

The significance function (score function )

S = Monte Carlo signal B = measured background

The control sample (important):



vs

(m-100MeV~m+200MeV)




The mass of Bc (mBc)



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)


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


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)


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



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)



Potential BcBs+h++X Branching ratio and

Bs CP measurement cross-check ~ O(103) Need investigation !


向 C. Rubbia 说明 Bc 介子产生的困难 , 需要 LHC（ 1992 ）


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！

+ ……


‘ 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：


‘ 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。


Thanks

2006-2-24bc meson physics1 chao-hsi chang ( 张肇西 ) i.t.p., chinese academy of sciences 1. the...

Documents