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

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