Complete Next-to-Next-to-Leading-Order QCD Correction to $J/\psi \to 3\gamma$ Decay

Abstract

We address the long-standing problem of negative decay and production rates in perturbative QCD for exclusive processes by proposing amplitude-level NRQCD factorization as a systematic prescription. Building on this, we present the first complete next-to-next-to-leading-order (NNLO) QCD correction to the decay $J/\psi \to 3\gamma$. The resulting partial width, $\Gamma(J/\psi \to 3\gamma) = 0.96^{+4.32}_{-0.13}$ eV, combines this NNLO contribution with the known up to $\mathcal{O}(\alpha_s v^2)$ relativistic correction and shows markedly improved agreement with the high-precision BESIII measurement. In the same way, $\Gamma(\Upsilon \to 3\gamma) = 0.0086^{+0.0028}_{-0.0006}$ eV is obtained. The dominant theoretical uncertainty originates from the renormalization scale variation, underscoring the challenge of perturbative convergence at this order and the necessity for future higher-order calculations.