Reconciling the nonrelativistic QCD prediction and the $J/\psi\to 3\gamma$ data

It has been a long-standing problem that the rare electromagnetic decay process $J/\psi\to 3\gamma$ is plagued with both large and negative radiative and relativistic corrections. To date it remains futile to make a definite prediction to confront with the branching fraction of $J/\psi\to 3\gamma$ recently measured by the \textsf{CLEO-c} and \textsf{BESIII} Collaborations. In this work, we investigate the joint perturbative and relativistic correction (i.e. the ${\mathcal O}(\alpha_s v^2)$ correction, where $v$ denotes the characteristic velocity of the charm quark inside the $J/\psi$) for this decay process, which turns out to be very significant. After incorporating the contribution from this new ingredient, with the reasonable choice of the input parameters, we are able to account for the measured decay rates in a satisfactory degree.