Annihilation rate of 2++ charmonium and bottomonium

Two-photon annihilation rates of 2+ tensor charmonium and bottomonium up to third radial excited states are estimated in the relativistic Salpeter method. Full Salpeter equation for 2+ tensor state is solved with a well defined relativistic wave function and we calculated the annihilation amplitude using the Mandelstam formalism. Our estimates of the decay widths are: Γ(χc2→2γ)=501 eV, Γ(χc2′→2γ)=534 eV, Γ(χb2→2γ)=7.4 eV and Γ(χb2′→2γ)=7.7 eV. We also give total decay widths of the lowest states estimated by the two-gluon decay rates, and the results are: Γtot(χc2)=2.64 MeV, Γtot(χb2)=0.220 MeV and Γtot(χb2′)=0.248 MeV.