Two-loop QCD corrections to gluon-gluon scattering

TL;DR

This work provides the O($\alpha_s^4$) virtual QCD corrections to gluon-gluon scattering by computing the interference of tree-level and two-loop amplitudes within conventional dimensional regularisation and the $\overline{\mathrm{MS}}$ scheme. The authors separate the result into infrared poles, predicted by Catani's factorisation, and a finite remainder expressed in real logarithms and polylogarithms, presenting a complete analytic form organized by powers of $N$ and $N_F$. These two-loop matrix elements complete the set needed for NNLO predictions of inclusive jet production, enabling more precise comparisons with hadron collider data. The paper also outlines the methodology for infrared cancellation with real-emission contributions and discusses remaining challenges related to initial-state radiation and higher-order splitting functions for full NNLO phenomenology.

Abstract

We present the O(alpha_s^4) virtual QCD corrections to gluon-gluon scattering due to the interference of tree and two-loop amplitudes. We work in conventional dimensional regularisation and give analytic expressions renormalised in the MSbar scheme. The structure of the infrared divergences agrees with that predicted by Catani while formulae for the finite remainder are given in terms of logarithms and polylogarithms that are real in the physical region. These results, together with those previously obtained for quark-quark and quark-gluon scattering, complete the two-loop matrix elements needed for the next-to-next-to-leading order contribution to inclusive jet production at hadron colliders.