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

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.

arXiv comment7 pages, 1 figure, version accepted for publication in PRD RC

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Cited by in corpus (7)

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• Resummation of relativistic corrections to exclusive productions of charmonia in e+ e- collisions
• Three Photon Decay of $J/\psi$ from Lattice QCD
• $\mathcal{O}({\alpha }_s{v}^2)$ corrections to hadronic decay of vector quarkonia
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• Relativistic corrections to ${\rm Y}$ exclusive decay into double $S-$wave charmonia
• Gauge invariant formulation of 3$\gamma$ decay of particle-antiparticle bound states