\begin{document}$ H \to J/\psi + \gamma $\end{document}, is a crucial channel for assessing the Yukawa coupling of the charm quark. In this article, we examine this process up to the next-to-next-to-leading order (NNLO) in QCD utilizing the Principle of Maximum Conformality (PMC). The PMC offers a systematic approach to eliminate renormalization scale uncertainties by resumming non-conformal β contributions into the QCD running coupling through the renormalization group equation (RGE). A PMC scale of \begin{document}$ Q_\star = 3.29\ {\rm{GeV}} $\end{document} is obtained, which reflects the low virtuality of the underlying QCD dynamics in the \begin{document}$ H \to J/\psi + \gamma $\end{document} process. Notably, this is an order of magnitude smaller than the scale estimated using the conventional method, i.e., \begin{document}$ \mu_r = m_H/2 $\end{document}. By removing the non-conformal \begin{document}$ \{\beta_i\} $\end{document}-terms from the perturbative QCD (pQCD) series, we observe that the PMC NLO QCD correction term is significantly enhanced, while the PMC NNLO QCD correction is suppressed. This indicates improved convergence of the pQCD series up to NNLO. Finally, we calculate the decay width \begin{document}$ \Gamma(H \to J/\psi + \gamma) = $\end{document}\begin{document}$ 14.183^{+0.249}_{-0.347} \pm 0.022 $\end{document} eV, where the first uncertainty arises from the factorization scale \begin{document}$ \mu_\Lambda \in [1, 2]\ {\rm{GeV}} $\end{document}, and the second is due to the estimation of unknown higher-order terms using the Pad\begin{document}$ \acute{e} $\end{document} approximant approach. The corresponding branching fraction is \begin{document}$ {\cal{B}}(H \to J/\psi + \gamma) = 3.485_{-0.161}^{+0.152} \times 10^{-6} $\end{document}."> Analysis of <i>H</i> → <i>J</i>/<i>ψ</i> + <i>γ</i> up to Next-to-Next-to-Leading order QCD corrections -
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