Annihilation Rate of Heavy 0^{++} P-wave Quarkonium in Relativistic Salpeter Method

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: $\mathrm{\Gamma }({\chi }_{c0}\to 2\gamma )=3.78$ keV, $\mathrm{\Gamma }({\chi }_{c0}^{\mathrm{\prime }}\to 2\gamma )=3.51$ keV, $\mathrm{\Gamma }({\chi }_{b0}\to 2\gamma )=48.8$ eV and $\Gamma(\chi’_{b0} \to 2\gamma)=50.3$ eV. We also give estimates of total widths by the two-gluon decay rates: ${\mathrm{\Gamma }}_{tot}({\chi }_{c0})=10.3$ MeV, ${\mathrm{\Gamma }}_{tot}({\chi }_{c0}^{\mathrm{\prime }})=9.61$ MeV, ${\mathrm{\Gamma }}_{tot}({\chi }_{b0})=0.887$ MeV and ${\mathrm{\Gamma }}_{tot}({\chi }_{b0}^{\mathrm{\prime }})=0.914$ MeV.