Two-loop QCD corrections to massless quark-gluon scattering

TL;DR

This work delivers the NNLO (O(αs^4)) virtual QCD corrections for massless 2→2 quark-gluon scattering, focusing on qq̄→gg and the crossed channels, using conventional dimensional regularization and MSbar renormalization. The authors separate the two-loop amplitude into infrared poles and a finite remainder, with the pole structure matching Catani’s universal factorization; the finite parts are provided analytically in terms of logarithms and polylogarithms and organized by color factors. They also compute the self-interference of one-loop amplitudes, expressed through master integrals in D=6−2ε and D=4−2ε, and confirm consistency with Catani’s framework. These results constitute essential building blocks for NNLO predictions of inclusive jet production at hadron colliders and pave the way for combining virtual and real-emission contributions with proper infrared cancellation. The analysis reinforces the feasibility of full NNLO jet cross sections and outlines the remaining steps, including gluon-gluon scattering and numerical implementations.

Abstract

We present the O(alphas^4) virtual QCD corrections to the scattering process of massless quark qqbar -> gg due to the interference of tree and two-loop amplitudes and to the self-interference of one-loop amplitudes. We work in conventional dimensional regularisation and our results are renormalised in the MSbar scheme. The structure of the infrared divergences agrees with that predicted by Catani while expressions for the finite remainder are given for the qqbar -> gg and the qg -> qg (gqbar -> gqbar) scattering processes in terms of logarithms and polylogarithms that are real in the physical region. These results, together with those previously obtained for quark-quark scattering, are important ingredients in the next-to-next-to-leading order contribution to inclusive jet production at hadron colliders.