Nonrelativistic QCD factorization and the velocity dependence of NNLO poles in heavy quarkonium production

We study the transition of a heavy quark pair from octet to singlet color configurations at next-to-next-to-leading order in heavy quarkonium production. We show that the infrared singularities in this process are consistent with nonrelativistic QCD factorization to all orders in the heavy quark relative velocity v. This factorization requires the gauge-completed matrix elements that we introduced previously to prove next-to-next-to-leading-order factorization to order v2