Electroweak corrections to $gg\rightarrow \gamma\gamma$

TL;DR

This paper calculates electroweak corrections to gluon fusion producing photon pairs, using advanced mathematical techniques, and finds small but significant effects relevant for LHC phenomenology.

Contribution

It introduces a semi-numerical method for evaluating complex Master Integrals in electroweak corrections to gluon fusion processes.

Findings

Corrections of around a few percent at the LHC.

Implementation of results into the MCFM Monte Carlo code.

Development of a semi-numerical evaluation technique for Master Integrals.

Abstract

We present the electroweak corrections for the production of a photon pair through gluon fusion, focusing on the contribution from the first two generations of quarks. The two-loop amplitude is calculated using a series of projection operators which define scalar form factors. In order to evaluate the Master Integrals which appear in this process we employ both generalized polylogarithms and Chen-iterated integrals. In order to perform a phenomenological study we develop a semi-numerical evaluation of the Master Integrals employing a fitting procedure to speed up the evaluation of burdensome higher weight contributions. We present results for the LHC, finding corrections of around a couple of percent to the leading order $gg \rightarrow \gamma\gamma$ process. Our results are implemented into the parton-level Monte Carlo code \texttt{MCFM}.