Gluon fragmentation into quarkonium at next-to-leading order

TL;DR

This paper calculates the next-to-leading order gluon fragmentation function into quarkonium, revealing significant corrections that alter the function's shape and increase the fragmentation probability, using a novel subtraction scheme.

Contribution

It introduces a new subtraction scheme for NLO calculations of gluon-to-quarkonium fragmentation functions, enabling phase-space integrals to be evaluated in four dimensions.

Findings

NLO corrections dramatically change the fragmentation function shape.

NLO corrections significantly increase the fragmentation probability.

All divergences are analytically canceled after renormalization.

Abstract

We present the first calculation at next-to-leading order (NLO) in $\alpha_s$ of a fragmentation function into quarkonium whose form at leading order is a nontrivial function of $z$, namely the fragmentation function for a gluon into a spin-singlet S-wave state at leading order in the relative velocity. To calculate the real NLO corrections, we introduce a new subtraction scheme that allows the phase-space integrals to be evaluated in 4 dimensions. We extract all ultraviolet and infrared divergences in the real NLO corrections analytically by calculating the phase-space integrals of the subtraction terms in $4-2\epsilon$ dimensions. We also extract the divergences in the virtual NLO corrections analytically, and detail the cancellation of all divergences after renormalization. The NLO corrections have a dramatic effect on the shape of the fragmentation function, and they significantly increase the fragmentation probability.