Annihilation Rate of $2^{++}$ Charmonium and Bottomonium

Abstract

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: $\Gamma ({\chi }_{c2}\to 2\gamma )=501$ eV, $\Gamma ({\chi }_{c2}^{\prime }\to 2\gamma )=534$ eV, $\Gamma ({\chi }_{b2}\to 2\gamma )=7.4$ eV and $\Gamma ({\chi }_{b2}^{\prime }\to 2\gamma )=7.7$ eV. We also give total decay widths of the lowest states estimated by the two-gluon decay rates, and the results are: ${\Gamma }_{tot}({\chi }_{c2})=2.64$ MeV, ${\Gamma }_{tot}({\chi }_{b2})=0.220$ MeV and ${\Gamma }_{tot}({\chi }_{b2}^{\prime })=0.248$ MeV.

Comments: 9 pages,1 figure, 3 tables