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

We compute the three-loop helicity amplitudes for qq¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ q\overline{q} $$\end{document} → 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 → qg amplitude shows the predicted factorized form from Regge theory and confirms previous results for the gluon Regge trajectory extracted from qq′ → qq′ and gg → gg scattering.