Three-loop helicity amplitudes for quark-gluon scattering in QCD

TL;DR

This paper presents the calculation of three-loop helicity amplitudes for quark-gluon scattering in massless QCD, providing important checks for infrared pole structures and confirming Regge theory predictions at high energies.

Contribution

It provides the first analytical three-loop helicity amplitudes for quark-gluon scattering in QCD, validating infrared pole structures and Regge theory predictions.

Findings

Confirmed the color quadrupole contribution to infrared poles.

Validated the Regge factorization at high energies.

Supported previous results on the gluon Regge trajectory.

Abstract

We compute the three-loop helicity amplitudes for $q\bar{q} \to gg$ and its crossed partonic channels, in massless QCD. Our analytical results provide a non-trivial check of the color quadrupole contribution to the infrared poles for external states in different color representations. At high energies, the $qg \to qg$ amplitude shows the predicted factorized form from Regge theory and confirms previous results for the gluon Regge trajectory extracted from $qq' \to qq'$ and $gg \to gg$ scattering.