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

Understand

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.