On the Resummation of Singular Distributions in QCD Hard Scattering

TL;DR

The paper addresses singular distributions arising at partonic threshold in QCD hard scattering and extends threshold resummation from color-singlet processes like Drell-Yan to general color exchanges. It develops a color-space factorization using soft Wilson lines and an anomalous-dimension matrix to resum soft gluon effects via ordered exponentials, with universal g1,g2 terms and color-dependent g3 terms that capture hard-scattering color exchange. The authors provide explicit formulations for the exponentiated soft contributions (E_{IJ}) and demonstrate the method through heavy-quark production in q qbar annihilation, including the explicit Γ matrix and its threshold simplifications, and outline extensions to gluon fusion and multi-jet final states. This framework enhances the reliability of perturbative QCD predictions near partonic threshold and sets the stage for systematic inclusion of nonleading soft logarithms across different hard-scattering channels.

Abstract

We discuss the resummation of distributions that are singular at the elastic limit of partonic phase space (partonic threshold) in QCD hard-scattering cross sections, such as heavy quark production. We show how nonleading soft logarithms exponentiate in a manner that depends on the color structure within the underlying hard scattering. This result generalizes the resummation of threshold singularities for the Drell-Yan process, in which the hard scattering proceeds through color-singlet annihilation. We illustrate our results for the case of heavy quark production by light quark annihilation, and briefly discuss its extension to heavy quark production through gluon fusion.