Three Photon Decay of $J/\psi$ from Lattice QCD

Three photon decay rate of $J/\psi$ is studied using two $N_f=2$ twisted mass gauge ensembles with lattice spacings $a\simeq 0.085$ fm (I) and $0.067$ fm(II). Using a new method, only the correlation functions directly related to the physical decay width are computed with all polarizations of the initial and final states summed over. Our results for such rare decay on the two ensembles are: $\mathcal{B}_{I,II}(J/\psi\rightarrow 3\gamma)=(1.614 \pm 0.016 \pm 0.261)\times 10^{-5},(1.809 \pm 0.051 \pm 0.295)\times 10^{-5}$ where the first errors are statistical and the second are estimates from systematics. We also propose a method to analyze the Dalitz plot of the corresponding process based on the lattice data which can provide direct information for the experiments.