Relativistic correction to gluon fragmentation function into pseudoscalar quarkonium

TL;DR

This paper calculates the relativistic correction to the gluon fragmentation function into eta_c mesons, enhancing understanding of eta_c production at high transverse momentum by employing multiple methods within the NRQCD framework.

Contribution

It introduces three distinct methods to compute the leading relativistic correction to the gluon to eta_c fragmentation function within NRQCD, and verifies existing results for charm quark fragmentation.

Findings

Calculated the relativistic correction to the gluon fragmentation function.

Verified the NLO result for charm quark fragmentation into eta_c.

Studied the evolution of fragmentation functions using DGLAP equations.

Abstract

Inspired by the recent measurements of the $\eta_c$ meson production at LHC, we investigate the relativistic correction effect for the fragmentation function of the gluon into $\eta_c$, which constitutes the crucial nonperturbative elements to understand $\eta_c$ production at high $p_T$. Employing three distinct methods, we calculate the leading relativistic correction to the $g\to\eta_c$ fragmentation function in the NRQCD factorization framework, as well as verify the existing NLO result for the $c\to \eta_c$ fragmentation function. We also study the evolution behavior of these fragmentation functions with the aid of DGLAP equation.