Next-to-next-to-leading-order QCD corrections to $\chi_{c0,2}\rightarrow \gamma\gamma$

TL;DR

This paper calculates NNLO QCD corrections to P-wave quarkonia decays into two photons, revealing significant discrepancies with experimental data and highlighting challenges in theoretical predictions within NRQCD.

Contribution

It provides the first semi-analytic NNLO corrections for P-wave quarkonia decay to two photons, including light-by-light contributions, and compares predictions with recent experimental results.

Findings

NNLO corrections are substantial and cause discrepancies with BESIII measurements.

Theoretical predictions fail to match the measured $ ext{chi}_{c2} o ext{gamma} ext{gamma}$ width.

Spin-dependent effects worsen the mismatch between theory and experiment.

Abstract

We calculate the next-to-next-to-leading-order (NNLO) perturbative corrections to $P$-wave quarkonia annihilation decay to two photons, in the framework of nonrelativistic QCD (NRQCD) factorization. The order-$\alpha_s^2$ short-distance coefficients associated with each helicity amplitude are presented in a semi-analytic form, including the "light-by-light" contributions. With substantial NNLO corrections, we find disquieting discrepancy when confronting our state-of-the-art predictions with the latest \textsf{BESIII} measurements, especially fail to account for the measured $\chi_{c2}\to\gamma\gamma$ width. Incorporating the effects of spin-dependent forces would even exacerbate the situation, since it lifts the degeneracy between the nonperturbative NRQCD matrix elements of $\chi_{c0}$ and $\chi_{c2}$ toward the wrong direction. We also present the order-$\alpha_s^2$ predictions to $\chi_{b0,2}\to\gamma\gamma$, which await the future experimental test.