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

TL;DR

This paper improves theoretical predictions for P-wave charmonium decay into two photons by applying high-order QCD corrections and the principle of maximum conformality, achieving better agreement with experimental data and emphasizing the importance of proper scale setting.

Contribution

It introduces a novel application of the PMC to NNLO QCD corrections for charmonium annihilation, reducing scale dependence and aligning predictions with BESIII measurements.

Findings

PMC reduces scale dependence in QCD predictions.

Predicted ratio matches BESIII measurements within errors.

Color-octet contributions further improve agreement.

Abstract

In this paper, we present a new analysis on the $P$-wave charmonium annihilation into two photons up to next-to-next-to-leading order (NNLO) QCD corrections by using the principle of maximum conformality (PMC). The conventional perturbative QCD prediction shows strong scale dependence and deviates largely from the BESIII measurements. After applying the PMC, we obtain a more precise scale-invariant pQCD prediction, which also agrees with the 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-octet contributions, even the central value can be in agreement with the data. This shows the importance of a correct scale-setting approach. We also give a prediction for the ratio involving $\chi_{b0, b2} \to\gamma\gamma$, which could be tested in future Belle II experiment.