The next-to-next-to-leading-order (NNLO) perturbative QCD (pQCD) predictions for both the decay width and the transition form factor in the ηc→γγ process, based on nonrelativistic QCD (NRQCD), deviate from precise experimental measurements. These significant discrepancies have cast doubt on the applicability of NRQCD to charmonium processes. In this paper, we analyze the ηc→γγ process by applying the principle of maximum conformality (PMC), a systematic method for eliminating renormalization scheme-and-scale ambiguities. The PMC renormalization scales are determined by absorbing the nonconformal β-terms that govern the behavior of the QCD running coupling via the renormalization group equation. We obtain the PMC scale Q⋆=4.49mc for the ηc→γγ decay width. Even after using the PMC method, the convergence of the pQCD series is still poor, which indicates the importance of uncalculated next-to-next-to-next-to-leading-order and higher-order terms. The resulting value for Γηc→γγ is in agreement with the Particle Data Group’s reported value of Γηc→γγ=5.1±0.4 keV within the bounds of uncertainties. Moreover, the transition form factor obtained using the PMC is also in good agreement with precise experimental measurements. The application of the PMC suggests a potential resolution to ηc→γγ puzzle and supports the applicability of NRQCD to charmonium processes. Published by the American Physical Society 2025
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