Order-v^4 Relativistic Corrections to Gluon Fragmentation into ^3S_1 Quarkonium

TL;DR

This paper calculates relativistic v^4 order corrections to gluon fragmentation into J/psi within NRQCD, revealing significant contributions from color-octet channels but a modest impact of v^4 corrections on overall production rates.

Contribution

It provides the first detailed calculation of order-v^4 relativistic corrections to gluon fragmentation into J/psi, including infrared divergence treatment and impact assessment.

Findings

Order-v^4 corrections enhance the color-singlet J/psi production rate.

Color-octet ^3P_J channel contributes significantly to J/psi production.

Relativistic corrections are less important than color-octet contributions in practice.

Abstract

We compute the relativistic corrections to the color-singlet contribution to gluon fragmentation into a J/psi at relative order v^4, making use of the nonrelativistic QCD (NRQCD) factorization approach. The corresponding full-QCD process exhibits infrared divergences that manifest themselves as single and double poles in epsilon in 4-2epsilon dimensions. We isolate the infrared-divergent contributions and treat them analytically. In the matching of full QCD to NRQCD, the pole contributions are absorbed into long-distance NRQCD matrix elements. The renormalizations of the ultraviolet divergences of the long-distance NRQCD matrix elements involve Born and one-loop single-pole counterterm contributions and Born double-pole counterterm contributions. While the order-v^4 contribution enhances the J/psi hadroproduction rate for the color-singlet channel substantially, this contribution is not important numerically in comparison with the color-octet contributions. We also find that the ^3P_J color-octet channel in the gluon fragmentation function contributes to J/psi hadroproduction significantly in comparison with the complete contribution of next-to-leading order in alpha_s in that channel.