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

TL;DR

This paper addresses the long-standing discrepancy between theoretical predictions and experimental measurements of the rare decay $J/ar{ ext{psi}} o 3 ext{gamma}$ by incorporating significant joint perturbative and relativistic corrections, achieving better agreement.

Contribution

It introduces the ${ m O}( ext{ extalpha}_s v^2)$ correction to the decay process, resolving previous prediction issues and aligning theory with recent experimental data.

Findings

Inclusion of ${ m O}( ext{ extalpha}_s v^2)$ correction significantly improves prediction accuracy.

The corrected theoretical decay rate matches experimental measurements satisfactorily.

Relativistic and radiative corrections are crucial for accurate $J/ar{ ext{psi}} o 3 ext{gamma}$ predictions.

Abstract

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.