Two-photon and two-gluon annihilation rates of P-wave scalar charmonium and bottomonium up to third radial excited states are estimated in the relativistic Salpeter method. We solved the full Salpeter equation with a well defined relativistic wave function and calculated the transition amplitude using the Mandelstam formalism. Our model dependent estimates for the decay widths: $\Gamma(\chi_{ c0} \to 2\gamma)=3.78$ keV, $\Gamma(\chi'_{ c0} \to 2\gamma)=3.51$ keV, $\Gamma(\chi_{ b0} \to 2\gamma)=48.8$ eV and $\Gamma(\chi'_{ b0} \to 2\gamma)=50.3$ eV. We also give estimates of total widths by the two-gluon decay rates: $\Gamma_{ tot}(\chi_{ c0})=10.3$ MeV, $\Gamma_{ tot}(\chi'_{ c0})=9.61$ MeV, $\Gamma_{ tot}(\chi_{ b0})=0.887$ MeV and $\Gamma_{ tot}(\chi'_{ b0})=0.914$ MeV.
Categories: hep-ph