Annihilation Rate of Heavy $0^{-+}$ Quarkonium in Relativistic Salpeter Method

Abstract

Two-photon and two-gluon annihilation rates of ${\eta }_c$, ${\eta }_c^{\prime }$, ${\eta }_b$ and ${\eta }_b^{\prime }$ are estimated in the relativistic Salpeter method. By solving the full Salpeter equation with a well defined relativistic wave function, we estimate $M_{{\eta }_c}=2.979\pm 0.432$ GeV, $M_{{\eta }_c^{\prime }}=3.566\pm 0.437$ GeV, $M_{{\eta }_b}=9.364\pm 1.120$ GeV and $M_{{\eta }_b^{\prime }}=9.941\pm 1.112$ GeV. We calculated the transition amplitude using the Mandelstam formalism and estimate the decay widths: $\Gamma ({\eta }_c\to 2\gamma )=7.14\pm 0.95$ KeV, $\Gamma ({\eta }_c^{\prime }\to 2\gamma )=4.44\pm 0.48$ KeV, $\Gamma ({\eta }_b\to 2\gamma )=0.384\pm 0.047$ KeV and $\Gamma ({\eta }_b^{\prime }\to 2\gamma )=0.191\pm 0.025$ KeV. We also give estimates of total widths by the two-gluon decay rates: ${\Gamma }_{tot}({\eta }_c)=19.6\pm 2.6$ MeV, ${\Gamma }_{tot}({\eta }_c^{\prime })=12.1\pm 1.3$ MeV, ${\Gamma }_{tot}({\eta }_b)=6.98\pm 0.85$ MeV and ${\Gamma }_{tot}({\eta }_b)=3.47\pm 0.45$ MeV.

Comments: 8 pages, 1 figure