Fragmentation, nonrelativistic QCD, and NNLO factorization analysis in heavy quarkonium production

We discuss heavy quarkonium production through parton fragmentation, including a review of arguments for the factorization of high-pT particles into fragmentation functions for hadronic initial states. We investigate the further factorization of fragmentation functions in the nonrelativistic QCD (NRQCD) formalism, and argue that this requires a modification of NRQCD octet production matrix elements to include non-Abelian phases, which makes them gauge invariant. We describe the calculation of uncanceled infrared divergences in fragmentation functions that must be factorized at next-to-next-to-leading order, and verify that they are absorbed into the new, gauge-invariant matrix elements.