1. 王国利（Guo-Li Wang） 哈尔滨工业大学
S波和P波重味介子衰变常数的计算
王国利（Guo-Li Wang）
哈尔滨工业大学

2. Introduction
Bethe-Salpeter and Salpeter Eequation
Wave Fuctions and Decay Constants
Numerical Results
Summary

3. Introduction Leptonic and Nonleptonic Weak Decay CKM Matrix Element
Neutral Mixing
e.x.,

4. Current Experimental Status

5. CLEO (2005)
BES (2005)

6. Traditional Nonrelativistic Approach in QM
S Wave: the decay constant is related to the wave function at origin in coordinate space
P Wave :the decay constant is related to the differential of wave function at origin

7. Our Notation
S Wave
P Wave

8. This talk is based on the following letters:
１，Phys. Lett. B596: 84-89, 2004
G.Cvetic, C.S.Kim, Guo-Li Wang, Wuk Namgung
２，Phys. Lett. B633: , 2006
Guo-Li Wang
３，Phys. Lett. B650: 15-21, 2007

9. Bethe-Salpeter and Salpeter Eequation
Bethe-Salpeter Equation:
Total momentum P and relative momentum q:
Normalization:

10. There is difficulty about the kernel, the time-inspired interaction?
Reduced version is needed (instantaneous).
The momentum is divided into two parts:
and the momenta :
will become to the and

11. Salpeter Eequation The reduced Bethe-Salpeter wave function:
and the useful notations

12. Salpeter wave function include four parts
And the Salpter equation can be written as:
Salpeter equation (positive and negative energy wave function)

13. Normalization:
We solve the full Salpeter equation will the simple Cornell potential:
In momentum space:

14. Wave Fuctions and Decay Constants
The wave functions for S wave meson in a nonralativistic model are:
In our model the relativistic wave function for a pseudoscalar meson

15. Since we have
The four wave functions are not independent
And the positive and negative wave function
And the normalization

16. Decay Constant of meson

17. Wave function for vector meson
There are only four independent wave functions
normalization

18. Decay Constant of meson

19. Wave function for meson
Normalization:
Decay constant

21. Wave function for meson
Normalization:
Decay constant

22. Wave function for meson
Normalization:
Decay constant

23. Numerical Results
1, Mass spectra of the mesons by fitting data and our best fit parameters

24. Decay constants of the mesons

26. 2, Mass spectra of the mesons

27. Decay constants of the mesons

29. Mass spectra of the P wave mesons

31. Decay constants of the P wave mesons

33. Summary
Relativistic corrections are important, especially for the P wave states.
The Decay Constants with successive radial excitation only fall slowly.

34. Thank you!