Annihilation Rate of Heavy 0^{++} 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: $\Gamma ({\chi }_{c0}\to 2\gamma )=3.78$ keV, $\Gamma ({\chi }_{c0}^{\prime }\to 2\gamma )=3.51$ keV, $\Gamma ({\chi }_{b0}\to 2\gamma )=48.8$ eV and $\Gamma ({\chi }_{b0}^{\prime }\to 2\gamma )=50.3$ eV. We also give estimates of total widths by the two-gluon decay rates: ${\Gamma }_{tot}({\chi }_{c0})=10.3$ MeV, ${\Gamma }_{tot}({\chi }_{c0}^{\prime })=9.61$ MeV, ${\Gamma }_{tot}({\chi }_{b0})=0.887$ MeV and ${\Gamma }_{tot}({\chi }_{b0}^{\prime })=0.914$ MeV.

arXiv comment8 pages, 1 figure, 4 tables

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• The electromagnetic decays of $X(3823)$ as the ${\psi }_2(1^3{D}_2)$ state and its radial excited states
• Why X(3915) is so narrow as a ${\chi }_{c0}(2P)$ state
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• Semileptonic transition of P wave bottomonium ${\chi }_{b0}(1P)$ to $B_c$ meson