Fragmentation functions of $g \rightarrow \eta_{c}$(¹S₀) and $g \rightarrow J/\psi$(³S₁) considering the role of heavy quarkonium spin

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 the literature, where the Braaten 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 model.