O(α_s v²) correction to pseudoscalar quarkonium decay to two photons

We investigate the $O(\alpha_s v^2)$ correction to the process of pseudoscalar quarkonium decay to two photons in nonrelativistic QCD (NRQCD) factorization framework. The short-distance coefficient associated with the relative-order $v^2$ NRQCD matrix element is determined to next-to-leading order in $\alpha_s$ through the perturbative matching procedure. Some technical subtleties encountered in calculating the ${O(\alpha_s)$ QCD amplitude are thoroughly addressed.