Fragmentation functions of $g\rightarrow \eta_c (^{1}S_0)$ and $g\rightarrow J/\psi (^{3}S_1)$ considering the role of heavy quarkonium spin

TL;DR

This paper analytically calculates the gluon fragmentation functions into $J/$ and $$ states, providing new explicit formulas and comparing different theoretical approaches to improve understanding of heavy quarkonium production.

Contribution

It presents the first analytical form of the gluon to $J/$ fragmentation function using Suzuki's model, contrasting with previous numerical approaches.

Findings

Universal fragmentation probability for $g  J/$ is about 10^{-6}

Analytical formulas align with previous numerical results

Different theoretical models yield consistent fragmentation probabilities

Abstract

The production of heavy quarkonia is a powerful tool to test our understanding of strong interaction dynamics. It is well-known that the dominant production mechanism for heavy quarkonia with large transverse momentum is fragmentation. In this work we, analytically, calculate the QCD leading order contribution to the process-independent fragmentation functions (FFs) for a gluon to split into the vector ($J/\psi$) and pseudoscalar ($\eta_c$) $S$-wave charmonium states. The analyses of this paper differ in which we present, for the first time, an analytical form of the $g\rightarrow J/\psi$ FF using a different approach (Suzuki's model) in comparison with other results presented in literatures, where the Braaten's scheme was used and the two-dimensional integrals were presented for the gluon FFs which must be evaluated numerically. The universal fragmentation probability for the $g\rightarrow J/\psi$ is about $10^{-6}$ which is in good consistency with the result obtained in the Braaten's model.