Higher-order relativistic corrections to gluon fragmentation into spin-triplet S-wave quarkonium

TL;DR

This paper calculates higher-order relativistic corrections to gluon fragmentation into quarkonium, revealing their relative importance and impact on phenomenology within the NRQCD framework.

Contribution

It provides the first detailed computation of order-v^4 relativistic corrections to gluon fragmentation into quarkonium in the 3S1 channel using NRQCD, including two-loop operator renormalization.

Findings

Order-v^4 corrections are enhanced but numerically small at current precision.

Gluon fragmentation into 3PJ color-octet quarkonium is significant compared to NLO contributions.

Infrared divergences are handled via subtractions absorbed into NRQCD matrix elements.

Abstract

We compute the relative-order-v^4 contribution to gluon fragmentation into quarkonium in the 3S1 color-singlet channel, using the nonrelativistic QCD (NRQCD) factorization approach. The QCD fragmentation process contains infrared divergences that produce single and double poles in epsilon in 4-2epsilon dimensions. We devise subtractions that isolate the pole contributions, which ultimately are absorbed into long-distance NRQCD matrix elements in the NRQCD matching procedure. The matching procedure involves two-loop renormalizations of the NRQCD operators. The subtractions are integrated over the phase space analytically in 4-2epsilon dimensions, and the remainder is integrated over the phase-space numerically. We find that the order-v^4 contribution is enhanced relative to the order-v^0 contribution. However, the order-v^4 contribution is not important numerically at the current level of precision of quarkonium-hadroproduction phenomenology. We also estimate the contribution to hadroproduction from gluon fragmentation into quarkonium in the 3PJ color-octet channel and find that it is significant in comparison to the complete next-to-leading-order-in-alpha_s contribution in that channel.