Lattice study of $J/\psi \rightarrow \gamma\eta_c$ using a method without momentum extrapolation

Abstract

We present a model-independent method to calculate the radiative transition without the momentum extrapolation for the off-shell transition factors. The on-shell transition factor is directly obtained from the lattice hadronic function. We apply the method to calculate the charmonium radiative transition $J/\psi \rightarrow \gamma\eta_c$. After a continuous extrapolation under three lattice spacings, we obtain the on-shell transition factor as $V(0)=1.90(4)$, where the error is the statistical error that already takes into account the $a^2$-error in the continuous extrapolation. Finally, we determine the branching fraction of $J/\psi\rightarrow \gamma \eta_c$ as $\operatorname{Br}(J/\psi\rightarrow \gamma\eta_c)=2.49(11)_{\textrm{lat}}(5)_{\textrm{exp}}$, where the second error comes from the uncertainty of $J/\psi$ total decay width $92.6(1.7)$ keV.