Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC

TL;DR

This work delivers the complete set of two-loop leading-colour QCD helicity amplitudes for $q\bar{q}\to g\gamma\gamma$ and $qg\to q\gamma\gamma$, supplying essential inputs for double-virtual QCD corrections to $\gamma\gamma j$ production at the LHC. The authors employ a helicity-projection framework, infrared factorisation with the $\mathbf{Z}$ operator, ultraviolet renormalisation in the $\overline{MS}$ scheme, and a finite-field reconstruction to obtain compact analytic expressions for the 2-loop finite remainders. Results are decomposed by colour/charge structures and organized in a minimal transcendental basis, with full analytic results published in supplementary material and benchmark numerical checks. Together with recent 3-loop and NNLO results, this work enables NNLO predictions for $\gamma\gamma j$ and potentially N3LO corrections to $\gamma\gamma$ production, sharpening Higgs-background estimates at hadron colliders.

Abstract

We calculate the complete set of two-loop leading-colour QCD helicity amplitudes for $γγj$-production at hadron colliders. Our results are presented in a compact, fully-analytical form.

Figures (1)

• Figure 1: Representative two-loop diagrams for the contributing colour/charge coefficients.