Fragmentation, NRQCD and NNLO Factorization Analysis in Heavy Quarkonium Production
Gouranga C. Nayak, Jian-Wei Qiu, George Sterman
TL;DR
The paper analyzes heavy quarkonium production at high transverse momentum via fragmentation, tying perturbative parton evolution to NRQCD-based nonperturbative matrix elements. It clarifies how fragmentation functions factorize into perturbative coefficients and NRQCD matrix elements, and shows that gauge invariance requires a gauge-completed NRQCD operator structure with Wilson lines. The authors identify infrared challenges that emerge at NNLO and demonstrate that the resulting divergences can be absorbed into the gauge-invariant matrix elements, strengthening NRQCD factorization at higher orders. While not a full all-orders proof, the work provides detailed methods for locating infrared behavior and performing two-loop calculations essential for validating fragmentation-based factorization of heavy quarkonium production.
Abstract
We discuss heavy quarkonium production through parton fragmentation, including a review of arguments for the factorization of high-p_T particles into fragmentation functions for hadronic initial states. We investigate the further factorization of fragmentation functions in the NRQCD formalism, and argue that this requires a modification of NRQCD octet production matrix elements to include nonabelian phases, which makes them gauge invariant. We describe the calculation of uncanceled infrared divergences in fragmentation functions that must be factorized at NNLO, and verify that they are absorbed into the new, gauge invariant matrix elements.