Electromagnetic annihilation rates of chi(c0) and chi(c2) with both relativistic and QCD radiative corrections

We estimate the electromagnetic decay rates of chi(c0)-->gamma gamma and chi c(2)-->gamma gamma by taking into account both relativistic and QCD radiative corrections. The decay rates are derived in the Bethe-Salpeter formalism and the QCD radiative corrections are included in accordance with the factorization assumption. Using a QCD-inspired interquark potential, we obtain relativistic BS wave functions of chi(c0) and chi(c2) by solving the BS equation for the corresponding (2S+1)L(J) states. Our numerical result for the ratio R=Gamma(chi(c0)-->gamma gamma)/Gamma(chi(c2)-->gamma gamma) is about 11-13, which agrees with the update E760 experiment data. Explicit calculations show that in addition to the QCD radiative corrections which may increase the ratio R by about a factor of 2, the relativistic corrections due to spin-dependent interquark forces induced by gluon exchange also enhance the ratio R substantially and its value is insensitive to the choice of parameters that characterize the interquark potential. Our expressions for the decay widths are identical with that obtained in the NRQCD theory to the next-to-leading order in upsilon(2) and alpha(s). Moreover, we have determined two new coefficients in the nonperturbative matrix elements for these decay widths.