Complete Next-to-Next-to-Leading-Order QCD Correction to $J/\ddot{I}ˆ\to 3{\hat{I}}^3$ 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 $J/\ddot{I}ˆ\to 3{\hat{I}}^3$. The resulting partial width, $\hat{I}“(J/\ddot{I}ˆ\to 3{\hat{I}}^3)=0.96_{-0.13}^{+4.32}$ eV, combines this NNLO contribution with the known up to $\mathcal{O}(\hat{I}{\pm }_s{v}^2)$ relativistic correction and shows markedly improved agreement with the high-precision BESIII measurement. In the same way, $\hat{I}“(\hat{I}\yen \to 3{\hat{I}}^3)=0.0086_{-0.0006}^{+0.0028}$ 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.