Annihilation rate of heavy [formula omitted] P-wave quarkonium in relativistic Salpeter method

Abstract

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 ( χ c 0 → 2 γ ) = 3.78 keV , Γ ( χ c 0 ′ → 2 γ ) = 3.51 keV , Γ ( χ b 0 → 2 γ ) = 48.8 eV and Γ ( χ b 0 ′ → 2 γ ) = 50.3 eV . We also give estimates of total widths by the two-gluon decay rates: Γ tot ( χ c 0 ) = 10.3 MeV , Γ tot ( χ c 0 ′ ) = 9.61 MeV , Γ tot ( χ b 0 ) = 0.887 MeV and Γ tot ( χ b 0 ′ ) = 0.914 MeV .