Fragmentation functions of $g\to {\eta }_c{(}^1{S}_0)$ and $g\to J\mathrm{/}\psi {(}^3{S}_1)$ considering the role of heavy quarkonium spin

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 ($J\mathrm{/}\psi$) 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 $g\to J\mathrm{/}\psi$ is about ${10}^{-6}$ which is in good consistency with the result obtained in the Braaten’s model.