$O({\alpha }_s{v}^2)$ correction to pseudoscalar quarkonium decay to two photons

Abstract

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.

Comments: v2, 28 pages, 2 figures and 2 tables, matching the published version; typos corrected, references added, as well as a "Note added in the proof"