Next-to-next-to-leading-order QCD corrections to χc0,2 → γγ

We calculate the next-to-next-to-leading-order perturbative corrections to P-wave quarkonia annihilation decay to two photons, in the framework of nonrelativistic QCD factorization. The order-alpha(2)(s) short-distance coefficients associated with each helicity amplitude are presented in a semianalytic form, including the light-by-light contributions. With sizable next-to-next-to-leading-order corrections, we find a disquieting discrepancy when confronting our state-of-the-art predictions with the latest BESIII measurements, which especially fail to account for the measured chi(c2) -> gamma gamma width. Incorporating the effects of spin-dependent forces would even exacerbate the situation, since it lifts the degeneracy between the nonperturbative nonrelativistic QCD matrix elements of chi(c0) and chi(c2) toward the wrong direction. We also present the order-alpha(2)(s) predictions to chi(b2) -> gamma gamma, which await the future experimental test.