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

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