Gluon fragmentation into quarkonium at next-to-leading order using FKS subtraction

TL;DR

This paper calculates the next-to-leading order gluon fragmentation function into heavy quarkonium using a subtraction scheme, revealing significant increases in fragmentation probabilities for eta_c and eta_b states.

Contribution

It introduces a NLO calculation of gluon fragmentation into quarkonium employing FKS subtraction, advancing precision in theoretical predictions.

Findings

NLO corrections increase fragmentation probabilities for eta_c and eta_b.

Analytical handling of divergences ensures accurate NLO results.

The method adapts FKS subtraction for heavy quarkonium fragmentation calculations.

Abstract

We present the calculation at next-to-leading order (NLO) in alpha_s of the fragmentation function of a gluon into heavy quarkonium in the color-octet spin-singlet S-wave channel. To calculate the real NLO corrections, we adapt a subtraction scheme introduced by Frixione, Kunszt, and Signer. Ultraviolet and infrared divergences in the real NLO corrections are calculated analytically by evaluating the phase-space integrals of the subtraction terms using dimensional regularization. The subtracted phase-space integrals are then evaluated in 4 space-time dimensions. The divergences in the virtual NLO corrections are also calculated analytically. After renormalization, all the divergences cancel. The NLO corrections significantly increase the fragmentation probability for a gluon into the spin-singlet quarkonium states eta_c and eta_b.