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

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.

arXiv comment74 pages, 9 figures, minor reorganization and clarifications, typos corrected, published version

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Cited by in corpus (6)

• Inclusive Production of Heavy Quarkonia in pNRQCD
• Inclusive Hadroproduction of $P$-Wave Heavy Quarkonia in Potential Nonrelativistic QCD
• Gluon fragmentation into ${}^3{P}_J^{[1,8]}$ quark pair and test of NRQCD factorization at two-loop level
• Resummation and renormalization of kinematical effects in inclusive $P$-wave quarkonium production
• Quarkonium production in pNRQCD: the $P$-wave case
• Resummation of threshold double logarithms in quarkonium fragmentation functions