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

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

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

Current Experimental Status

CLEO (2005) BES (2005)

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

Our Notation S Wave P Wave

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: 492-496, 2006 Guo-Li Wang ３，Phys. Lett. B650: 15-21, 2007

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

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

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

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

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

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

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

Decay Constant of meson

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

Decay Constant of meson

Wave function for meson Normalization: Decay constant

Wave function for meson Normalization: Decay constant

Wave function for meson Normalization: Decay constant

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

Decay constants of the mesons

2, Mass spectra of the mesons

Decay constants of the mesons

Mass spectra of the P wave mesons

Decay constants of the P wave mesons

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

Thank you!