Two-Loop Amplitudes for Gluon Fusion into Two Photons

TL;DR

This paper addresses the irreducible QCD background to Higgs searches in the $H \to \gamma\gamma$ channel by computing the two-loop matrix elements for $gg \to \gamma\gamma$ with massless quarks in the loop and the crossed process $g\gamma \to g\gamma$. A unitarity/cut-based approach in dimensional regularization is used with Catani's infrared factorization, yielding ${\cal M}^{(2)} = {\cal I}^{(1)}\,{\cal M}^{(1)} + {\cal M}^{(2)\rm fin}$ for the two processes. The finite remainders are given analytically for all helicities in terms of logarithms and polylogarithms up to ${\rm Li}_4$, with kinematics encoded in $x=t/s$, $y=u/s$, $X=\ln(-t/s)$ and $Y=\ln(-u/s)$, and include sums over quark charges $\sum Q_i^2$. These results, together with the one-loop $gg \to \gamma\gamma g$ amplitudes, enable a substantial reduction in the theoretical uncertainty of the QCD background to Higgs production at the LHC and will feed into forthcoming Higgs background studies. The work also provides the crossed-channel results for $g\gamma \to g\gamma$ and discusses scheme conventions (HV vs CDR) and the unitarity-based computation of master integrals.

Abstract

We present the two-loop matrix elements for the scattering of two gluons into two photons in QCD. These matrix elements will enter into improved estimates of the QCD background to Higgs production at the LHC when the Higgs decays into two photons. The photon mode is especially important if M_H < 140 GeV. We also give the amplitudes for the crossed process, glue gamma to glue gamma.