Covariant calculation of a two-loop test of nonrelativistic QCD factorization

TL;DR

This paper performs a covariant two-loop calculation to test the NRQCD factorization conjecture for quarkonium production, confirming its validity and exploring differences with previous light-cone calculations.

Contribution

It provides the first covariant two-loop calculation of the NRQCD long-distance matrix element for heavy-quark pairs, supporting the universality aspect of the factorization conjecture.

Findings

Infrared divergences are independent of Wilson line direction.

Results are consistent with NRQCD factorization.

Differences with previous light-cone calculations are identified.

Abstract

We test the nonrelativistic QCD factorization conjecture for inclusive quarkonium production at two loops by carrying out a covariant calculation of the nonrelativistic quantum chromodynamics (NRQCD) long-distance matrix element (LDME) for a heavy-quark pair in an $S$-wave, color-octet state to fragment into a heavy-quark pair in a color-singlet state of arbitrary orbital angular momentum. The NRQCD factorization conjecture for the universality of the LDME requires that infrared divergences that it contains be independent of the direction of the Wilson line that appears in its definition. We find this to be the case in our calculation. The results of our calculation differ in some respects from those of a previous calculation that was carried out by Nayak, Qiu, and Sterman using light-cone methods. We have identified the sources of some of these differences. The results of both calculations are consistent with the NRQCD factorization conjecture. However, the general principle that underlies this confirmation of NRQCD factorization at two-loop order has yet to be revealed.