Fragmentation function of $g\to Q\bar{Q}(^3S_1^{[8]})$ in soft gluon factorization and threshold resummation

TL;DR

This paper develops a new approach using soft gluon factorization to calculate the gluon fragmentation function into a color-octet $^3S_1$ quark-antiquark pair, incorporating threshold resummation for improved accuracy.

Contribution

It introduces the SGF framework for this fragmentation function, computes the hard part at NLO, and derives a renormalization group equation to resum threshold logarithms, improving upon NRQCD methods.

Findings

SGF resums velocity corrections important for phenomenology

NLO calculation of the hard part in the SGF framework

Resummation of threshold logarithms via RG equation

Abstract

We study the fragmentation function of the gluon to color-octet $^3S_1$ heavy quark-antiquark pair using the soft gluon factorization (SGF) approach, which expresses the fragmentation function in a form of perturbative short-distance hard part convoluted with one-dimensional color-octet $^3S_1$ soft gluon distribution (SGD). The short distance hard part is calculated to next-to-leading order in $\alpha_s$ and a renormalization group equation for the SGD is derived. By solving the renormalization group equation, threshold logarithms are resummed to all orders in perturbation theory. The comparison with gluon fragmentation function calculated in NRQCD factorization approach indicates that the SGF formula resums a series of velocity corrections in NRQCD which are important for phenomenological study.