1. The Color Octet Effect from at B Factorry
The 3rd Workshop on Heavy Quarkonium, Oct , 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

2. 1. Brief Introduction to FDC-NRQCD package
Feynman Diagram Calculation(FDC), This project was started at 1993.
FDC homepage:
FDC-SM-and-Many-Extensions
FDC-NRQCD
FDC-MSSM
FDC-EMT
FDC-PWA
Written in REDUCE,
RLISP and C++.
To create Fortran.

3. 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

4. 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

5. NRQCD calculations performed by using FDC-NRQCD package
Presented in this talk,
Hep-ph/
C.F. Qiao and J. X. Wang,
PRD 69, ,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.
………….

6. >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

8. 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, (2001).
BELLE Collaboration, K.~Abe et al.,
PRL 88, (2002).

12. 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.

13. 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/ ].
tried on it for the $J/\psi$ production at B factory and broadened
the $p^*$ spectra from color octet $J/\psi$.

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

18. 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

19. The results for

20. The results for with cut-off

21. 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.

22. 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.