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

TL;DR

This paper calculates the next-to-leading order QCD correction at order $\alpha_s v^2$ to the decay of pseudoscalar quarkonium into two photons within the NRQCD framework, addressing technical challenges in the amplitude computation.

Contribution

It provides the first detailed calculation of the $O(\alpha_s v^2)$ correction to pseudoscalar quarkonium decay to two photons, including the determination of the associated short-distance coefficient.

Findings

The $O(\alpha_s v^2)$ correction is explicitly computed.

Technical subtleties in the QCD amplitude calculation are resolved.

The results improve the precision of theoretical predictions for quarkonium decay processes.

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.