NLO fragmentation functions for a quark into a spin-singlet quarkonium: Same flavor case

TL;DR

This paper calculates the next-to-leading-order fragmentation functions for a charm or bottom quark into the corresponding spin-singlet quarkonium states, providing more accurate tools for quarkonium production predictions.

Contribution

It presents the first NLO QCD calculations of fragmentation functions for a quark into a spin-singlet quarkonium, including detailed numerical results and scale sensitivity analysis.

Findings

NLO corrections are significant for the fragmentation functions.

Fragmentation functions are provided as figures and fitting functions.

Explicit analysis of scale sensitivities.

Abstract

In the paper, we calculate the fragmentation functions for $c \to \eta_c$ and $b \to \eta_b$ up to next-to-leading-order (NLO) QCD accuracy. The ultraviolet divergences in the real corrections are removed through operator renormalization under the modified minimal subtraction scheme. We then obtain the fragmentation functions $D_{c \to \eta_c}(z,\mu_F)$ and $D_{b \to \eta_b}(z,\mu_F)$ up to NLO QCD accuracy, which are presented as figures and fitting functions. The numerical results show that the NLO corrections are significant. The sensitives of the fragmentation functions to the renormalization scale and the factorization scale are analyzed explicitly.