The Color Octet Effect from at B Factorry The 3rd Workshop on Heavy Quarkonium, Oct. 12-15, Beijing The Color Octet Effect from at B Factorry Jian-Xiong Wang IHEP, Beijing Brief Introduction to FDC-NRQCD package Motivation Uncertainty in the theoretical treatmeant for production The results for Conclusion

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 System FIG.1: FDC system flow chart Input for physical process Input for physical model Input for physical process Choose physical model and processes Feynman diagram generation Physical model evaluation Amplitude manipulation Full Feynman Rules Counter-terms Physical parameters Treatment of kinematics Numerical integration Latex version of then model Numerical results & Required plots in Hbook format FIG.1: FDC system flow chart

NRQCD Formulation Fwuvy Theorem Color Factor Gauge Invariant Check 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

NRQCD calculations performed by using FDC-NRQCD package Presented in this talk, Hep-ph/0311292 C.F. Qiao and J. X. Wang, PRD 69, 014015,2004 At Tevatron, Presented in C. F. Qiao’s talk At Tevatron and LHC, will presented in C. H. Chang’s talk Is the largest calculation performed by using FDC-NRQCD until now. ………….

>process_cp old new >diag >amp >kine >cd fort >make Calculation of One Physical Process >process_cp old new >diag >amp >kine >cd fort >make >int Examples for integrated multi-processes calculation tool

The Problem for the universal NRQCD matrix elements CDF Collaboration, F.~Abe {\it et al.} PRL. 69, 3704 (1992);79, 572 (1997); 79, 578 (1997); BABAR Collaboration, B.~Aubert et al., PRL. 87, 162002 (2001). BELLE Collaboration, K.~Abe et al., PRL 88, 052001 (2002).

The measurement of the J/\psi$ production at B factory in BaBar and 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 $J/\psi$.

The numerical results of the total cross section For Color-Singlet: For Color-Octet: Where the condition for hard photon is used.

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

The results for

The results for with cut-off

The Property of the Spectrum: It is hardly changed even if there is lage QCD correction. It can not be changed by the procedure of and gluon handronization into and handron. It is very clearly separate the color octet and color singlet signal. Another advantage is that the color octet cross section is even 61% large than it’s Born one.

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.