Fragmentation function of gluon into spin-singlet $P$-wave quarkonium

TL;DR

This paper calculates the gluon-to-$h_c$ fragmentation function at leading order in NRQCD, providing an analytical, infrared-finite result and estimating the fragmentation probability to be around 10^{-6}.

Contribution

It presents the first analytical calculation of the gluon-to-$h_c$ fragmentation function using modern multi-loop techniques within NRQCD.

Findings

Fragmentation probability estimated at ~10^{-6}.

Analytical, infrared-finite short-distance coefficient derived.

First calculation of this kind for $h_c$.

Abstract

Following the operator definition of the fragmentation function developed by Collins and Soper, we compute the gluon-to-$h_c$ fragmentation function at the lowest order in the velocity expansion in NRQCD factorization approach. Utilizing some modern technique developed in the area of multi-loop calculation, we are able to analytically deduce the infrared-finite color-singlet short-distance coefficient associated with the fragmentation function. The fragmentation probability for gluon into $h_c$ is estimated to be order $10^{-6}$.