The Color Octet Effect from at B Factorry

Jian-Xiong Wang

IHEP, Beijing

1. Brief Introduction to FDC-NRQCD package

2. Motivation

3. Uncertainty in the theoretical treatmeant for production

4. The results for

5. Conclusion

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The 3rd Workshop on Heavy Quarkonium, Oct. 12-15, Beijing

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1. Brief Introduction to FDC-NRQCD package

Feynman Diagram Calculation(FDC), This project was started at 1993.

FDC homepage: http://www.ihep.ac.cn/lunwen/wjx/public_html/index.html

FDC-SM-and-Many-Extensions FDC-NRQCD FDC-MSSM FDC-EMT FDC-PWA

Written in REDUCE,RLISP and C++.To create Fortran.

FDC SystemFDC System

Numerical results &Required plots in Hbook format

Numerical results &Required plots in Hbook format

Physical model evaluationPhysical model evaluation

Full Feynman RulesCounter-termsPhysical parameters

Full Feynman RulesCounter-termsPhysical parameters

Latex version of then modelLatex version of then model

Input for physical modelInput for physical model

Numerical integrationNumerical integration

Treatment of kinematicsTreatment of kinematics

Amplitude manipulationAmplitude manipulation

Feynman diagram generationFeynman diagram generation

Input for physical processChoose physical modeland processes

Input for physical processChoose physical modeland processes

FIG.1: FDC system flow chartFIG.1: FDC system flow chart

3. FDC-NRQCD

Hevay Quark Meson: J/psi, B_c, ...... S-wave, P-wave Color-singlet, Color Octet

NRQCD Formulation Fwuvy Theorem

Color Factor Gauge Invariant Check

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cbPPBpPP Jc ),()( 01

2,1,03

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NRQCD calculations performed by using FDC-NRQCD package

At Tevatron, Presented in C. F. Qiao’s talk

At Tevatron and LHC, will presented in C. H. Chang’s talk

C.F. Qiao and J. X. Wang, PRD 69, 014015,2004

Presented in this talk,Hep-ph/0311292

………….

gcbBpPP c )( Is the largest calculation performed by using FDC-NRQCD until now.

Calculation of One Physical Process ● >process_cp old new ● >diag

● >amp

● >kine● >cd fort

● >make

● >int

Examples for integrated multi-processes calculation tool

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The Problem for the universal NRQCD matrix elements

BABAR Collaboration, B.~Aubert et al.,PRL. 87, 162002 (2001).

BELLE Collaboration, K.~Abe et al.,PRL 88, 052001 (2002).

CDF Collaboration, F.~Abe {\it et al.}PRL. 69, 3704 (1992);79, 572 (1997);79, 578 (1997);

The measurement of the J/\psi$ production at B factory in BaBarand Belle experiments\cite show that the theoretical predication

E. Braaten and Y. Q. chen, PRL 76, 730 (1996)Peter Cho, Adam K. Leibovich, PRD 53, 6203 (1996); PRD54, 6690 (1996).

For $p^*_{J/\psi}$ spectra did not agree with experimental results,The color octet processes only contribute to the endpoint of $p^*_{J/\psi}$ Spectra due to the kinematics of the two body final state. But the experiments did not observe the this signal.

To explain this discrepancy, it is nature to think that $J/\psi^{(8)}$ have to hadronize into color singlet $J/\psi$ and will lose it's energy such as the case when a quark jet hadronize into hadrons. Therefore there should be a hadronization possibility function $F(x,...)$ for $J/\psi$ production with momentum $p_{J/\psi}=x~p_{J/\psi^{(8)}}$ and $\int^1_0dx~F(x,...)=1$. The universal NRQCD matrix elements treatment is just a first step approximation of $F(x,...)=\delta(1-x)$.

S.~Fleming, A. K. Leibovich and T. Mehen.[arXiv:hep-ph/0306139].

tried on it for the $J/\psi$ production at B factory and broadened the $p^*$ spectra from color octet $J/\psi$.

,445.0)/( pbXJee

,128.0)/( pbXJee

,233.0)/( pbXJee

pbXJee 2.0)/(

The numerical results of the total cross section

For Color-Singlet:

For Color-Octet:

Where the condition for hard photon is used.MeVE 100

The reason is very clear that the following cross sections increase when

the center mass energy of go down from 10.6GeV to 5GeV.

will closed.

increase 4 times

increase 51 times

increase 17 times

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gSee ][ 01)8(

The results for XJee /

,445),/( fboctetcolorXJee ,128)sin,/( fbgletcolorXJee

The results for with cut-off XJee /

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The Property of the Spectrum:

1. It is hardly changed even if there is lage QCD correction.

2. It can not be changed by the procedure of and gluon handronization into and handron.

3. It is very clearly separate the color octet and color singlet signal.

4. Another advantage is that the color octet cross section is even 61% large than it’s Born one.

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Conclusion

A good way is shown to clarify the situation of the

Color-Octet Mechanism for production:

To measure the Spectrum in the initial state radiation

Process , It could avoid the

uncertainty from handronization and

QCD correction.

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