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In this paper, we present a new analysis on the $P$-wave charmoniumannihilation into two photons up to next-to-next-to-leading order (NNLO) QCDcorrections by using the principle of maximum conformality (PMC). Theconventional perturbative QCD prediction shows strong scale dependence anddeviates largely from the BESIII measurements. After applying the PMC, weobtain a more precise scale-invariant pQCD prediction, which also agrees withthe BESIII measurements within errors, i.e.$R={\Gamma_{\gamma\gamma}(\chi_{c2})}/{\Gamma_{\gamma\gamma}(\chi_{c0})}=0.246\pm0.013$, where the error is for$\Delta\alpha_s(M_\tau)=\pm0.016$. By further considering the color-octetcontributions, even the central value can be in agreement with the data. Thisshows the importance of a correct scale-setting approach. We also give aprediction for the ratio involving $\chi_{b0, b2} \to\gamma\gamma$, which couldbe tested in future Belle II experiment.

The $P$-wave charmonium annihilation into two photons $\chi_{c0, c2}\rightarrow \gamma\gamma$ with high-order QCD corrections