Annihilation rate of heavy 0++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: Γ(χc0→2γ)=3.78 keVΓ(χc0→2γ)=3.78 keV, Γ(χc0′→2γ)=3.51 keV, Γ(χb0→2γ)=48.8 eVΓ(χb0→2γ)=48.8 eV and Γ(χb0′→2γ)=50.3 eV. We also give estimates of total widths by the two-gluon decay rates: Γtot(χc0)=10.3 MeVΓtot(χc0)=10.3 MeV, Γtot(χc0′)=9.61 MeV, Γtot(χb0)=0.887 MeVΓtot(χb0)=0.887 MeV and Γtot(χb0′)=0.914 MeV.