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

Two-photon and two-gluon annihilation rates of $\eta_c$, $\eta'_c$, $\eta_b$ and $\eta'_b$ 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, $M_{\eta'_c}=3.566\pm 0.437$ GeV, $M_{\eta_b}=9.364\pm 1.120$ GeV and $M_{\eta'_b}=9.941\pm 1.112$ 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, $\Gamma(\eta'_c \to 2\gamma)=4.44\pm 0.48$ KeV, $\Gamma(\eta_b \to 2\gamma)=0.384\pm 0.047$ KeV and $\Gamma(\eta'_b \to 2\gamma)=0.191\pm 0.025$ KeV. We also give estimates of total widths by the two-gluon decay rates: $\Gamma_{tot}(\eta_c)=19.6\pm 2.6$ MeV, $\Gamma_{tot}(\eta'_c)=12.1\pm 1.3$ MeV, $\Gamma_{tot}(\eta_b)=6.98\pm 0.85$ MeV and $\Gamma_{tot}(\eta_b)=3.47\pm 0.45$ MeV.