2005-6-20C.H. Chang, ITP, AS Beijing1 Chao-Hsi Chang ( 张肇西 Zhao-XiZhang) [email protected]...

2005-6-20 C.H. Chang, ITP, AS Beijing 1

Chao-Hsi Chang ( 张肇西 Zhao-XiZhang) [email protected]

I.T.P., Chinese Academy of Sciences 1. Introduction (the meson Bc & it

s mass)2. Decay (lifetime, …)3. Production (Tevatron vs LHC)4. Outlook

Production and decay of the meson Bc

—— A brief review of theoretical studies ——

(Based on the collaboration with Y.-Q. Chen, X.-Q. Li, C.-D. Lu, C.-F. Qiao, G.-L. Wang, J.-X. Wang, X.-G. Wu, et al)


1. Introduction (the meson Bc & its mass)

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-flavor mesons (unique in SM)

(weak decay only)

Very similar to, and very different from, hidden flavored heavy quarkonium J/ψ, ηc, …,Υ,ηb…. Good and new object for tests of PM, NRQCD, Lattice results etc.



Bc mass : Lattice QCD : I.F. Allison et al, PRL 94 172001.

PM: Y.Q. Chen &Y.P. Kuang, PRD 46, 1165; Eichten & C.Quigg, PRD 49, 5845;….:

A. Kronfeld’s talk



Theoretical estimate & LEP-I (ALAPH, PLB 402, 213; DELPHI PLB 398, 207): experimental studies of Bc can be carry out at Tevatron and LHC only!

Theoretical estimate at Z resonance (LEP-I) :

OPAL result PLB 420, 157:

The “early” day’s results



• CDF discovery (1998 Observation) PRD 58, 112004

- 110 Pb-1 data ECM=1.8 TeV RunI Bc± J/(+-) ±

- The only previous evidence by CDF RunI

• CDF new Observation hep-ex/0505076

Bc± J/(+-) ± - 360 Pb-1 data ECM=1.96 TeV, RunIImBc=6287.0±4.8(stat)±1.1(syst) MeV/c2, 18.9±5.7 events

• D0 new Observation ICHEP-04 & Fermilab 4539-CONF

- 200 Pb-1 data ECM=1.96 TeV, RunII Bc± J/(+-) ±

Mass: 5.95 ± 0.34 GeV/c2

Events: 95 ± 12±11 +0.14

-0.13

Lifetime: 0.448 +0.123 ± 0.121 ps-0.096

- Br~2.4% + trilepton final state + easy to trigger

Note: even Br(Bc± J/(+-) ± )/Br(Bc± J/(+-) ± ) not available !

Present experimental status:


2. Decay

Bc lifetime: weak decay only (no strong &EM direct decay) according to spectator model and B & D mesons’ lifetime and annihilation: one may estimate More careful estimate:

vertex detector is useful in observation

Decay: Pure (radiative) leptonic Semoleptonic Nonleptonic


2. Decay

:

:

Bc lifetime (non-spectator effects involved)

: :

( )

In comparison with D & B mesons (input), we obtain:


2. Decay• Pure leptonic (radiative) decay (about measurement of the decay constant fBc):

Pure leptonic (tree) decay: (chiral suppression)

Radiative leptonic decay (decay constant):(escaped from chiral suppression)

QED corrections (one-loop):


2. DecayRadiative leptonic decay (QED correction to the tree level) in total:

Photon spectrum:

It is quite difficult for hadronic expt. to measure the decay constant!


2. Decay• Leptonic decay with light hadrons (color-singlet vs color-octet):

Color-singlet:

Short distance:

Long distance:

Charge lepton spectrum:

In the decay


2. DecayColor-octet:

P-wave (color-octet)

S-wave(color-octet)

Color-singlet

Near the endpoint of the charged lepton in the decay to observe the color-octet components!

Charged lepton spectrum:


2. Decay

• Semileptonic decays :

Transitions (decays with great momentum recoil)

The key factor:


2. Decay

Mandelstam formulation (or say composite quantum field theory) to

deal with the recoil effects in transitions:

The ‘wave function’ of bound state equation:

To cover a great range of momentum transfer (recoil), BS equation seems to be one of good choices for the problem.


2. Decay

Carry out the contour integrations & :


2. Decay

The semileptonic decays (S-wave) :

One I-W function


2. Decay

The semileptonic decays (P-wave or ) :

Two I-W functions

Recoil one

Normal one

Spectrum of charged lepton in the decays:


2. Decay

Nonleptonic decays (S-wave product): EFT+Factorrization


2. DecayNonleptonic decays (P-wave product or ):


2. Decay

•The lifetime is ‘quite long’ that the vertices of production and decay can be measured by vertex detector experimentally• Sizable decay channels are rich• The branch ratio of the decay to is quite great (form factors)• The branch ratio of decay to or is very large• Study two flavor ‘simultaneously’ (Vcb & Vcs)• Radiative pure leptonic decays escape from chiral suppression, but to measure the decay constant is still difficult • The color-octet component might be observable through • …….


3. Production (Tevatron & LHC)

Gluon-gluon fusion mechanism dominant

36 Feynman diagrams for complete calculations

‘Complete LO computation’: information about the accompany quark-jets is kept

QCD factorization:

Subprocess:



The lowest order calculations: uncertainties from

The cross-section at LHC is greater than that at Tevatron

S-wave state production



LHC

Tevatron

Uncertainty from mC



and

Uncertainty

from PDFs



Uncertainties: quite great; sensitive to Q2, mc . High order calculation can suppress them but it is too complicated.

Uncertainty from


3. Production (Tevatron & LHC)P-wave excited state productionTo 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

P-wave production ( color-singlet)

To see the contributions to Bc

& the P-wave characters


| |2| |2 | |2


Color octet may be comparable with that of color singlet

Color-singlet (P-wave) M.E.

Color-octet (S-wave) M.E.

Scaling rule of NRQCD:



LHC

Tevatron

Color-octet 1S0

Color-octet 3S1

Color-singlet 3P2

Color-singlet 1P1

Color-singlet 3P0

Color-singlet 3P1

P-wave production color-singlet vs color-octetColor-octet


• The cross section of Bc at LHC is greater than that at Tevatron by one and more order of magnitude• The uncertainties are quite big for LO PQCD• The cross section is at the order 10-3 (less) of B meson production


Experimental needs of the M.C. generator:Difficulties of the experiments in Hadronic Collider

High efficiency for the generator

Generator: BCVEGPY1.0 (S-wave, helicity techniques )

BCVEGPY2.0 (S,P-wave, Color-octet,…& Mixture)

Signals for feasibility studies

CPC Lib. & hppt://www.itp.ac.cn/~zhangzx/



(ours)another

The generator is tested by comparing with PYTHIA

The generator is proved to be suitable for the original purpose.



- 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%)

- Bc Bs associated h+ (as a tag for Bs).

- Br[ BcBs +h+ +X ] as Bs CP violation source ? Bc decay vertex is crucial .

To be a possible source for tagged Bs (at LHC) ?



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%The from the other side b-quark fragmentation Muon + opposite 2nd VTX (on Ds)

under feasibility investigation !


4. Outlook

• Experimental studies on Bc meson have been started at Tevatron

already, and fresh results will be issued ‘from time to time’.• The production cross-section at LHC is greater than that at

Tevatron, so further experimental studies at LHC can be expected.• Some model predictions will be tested.• Theoretical estimates are requested to decrease the uncertainties

and to increase the precision with data being accumulated.• Bc studies may solve some puzzles relating to charmonium

e.g. the observation may clarify up some of contents

in , in meson there are more charm quarks than in meson.

and some ‘unexpected things’ might be found.• ……


Thanks

2005-6-20C.H. Chang, ITP, AS Beijing1 Chao-Hsi Chang ( 张肇西 Zhao-XiZhang) [email protected]...

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