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$O(α_s v^2)$ correction to pseudoscalar quarkonium decay to two photons

We investigate the $O(α_s v^2)$ 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 $α_s$ through the perturbative matching procedure. Some technical subtleties encountered in calculating the ${O(α_s)$ QCD amplitude are thoroughly addressed.