NRQCD Factorization and Velocity-dependence of NNLO Poles in Heavy Quarkonium Production
Gouranga C. Nayak, Jian-Wei Qiu, George Sterman
TL;DR
NRQCD factorization for heavy quarkonium production hinges on separating short-distance and long-distance physics, but a complete proof remains elusive. The authors extend the NNLO eikonal analysis to finite relative velocity v and employ gauge-completed NRQCD matrix elements with Wilson lines to all orders in v. They find that the NNLO infrared pole for octet-to-singlet transitions factors into a color factor times a velocity-dependent universal function I^(8->1)(v,ε) and is independent of the Wilson line direction, generalizing previous v^2 results and providing an explicit expression for I. This supports NRQCD factorization at NNLO for arbitrary v, clarifies the role of Wilson lines in nonrelativistic factorization, and motivates further study of spin-dependent operators.
Abstract
We study the transition of a heavy quark pair from octet to singlet color configurations at next-to-next-to-leading order (NNLO) in heavy quarkonium production. We show that the infrared singularities in this process are consistent with NRQCD 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 NNLO factorization to order v ^2.