Two-loop mixed QCD-EW corrections to $gg \to Hg$

TL;DR

This paper calculates the two-loop mixed QCD-Electroweak corrections to Higgs plus gluon production via gluon fusion, providing explicit expressions and numerical tools for improved precision in theoretical predictions.

Contribution

It introduces a novel calculation of two-loop mixed QCD-EW corrections for gg to Hg, including explicit polylogarithmic expressions and simplified helicity amplitudes.

Findings

Both helicity amplitudes are finite.

A weight drop occurs when all gluons share the same helicity.

Provided optimized expressions for numerical evaluation.

Abstract

We compute the two-loop mixed QCD-Electroweak (QCD-EW) corrections to the production of a Higgs boson and a gluon in gluon fusion. The relevant four-point functions with internal massive propagators are expressed as multiple polylogarithms with algebraic arguments. We perform the calculation by integration over Feynman parameters and, independently, by the method of differential equations. We compute the two independent helicity amplitudes for the process and we find that they are both finite. Moreover, we observe a weight drop when all gluons have the same helicity. We also provide a simplified expression for the all-plus helicity amplitude, which is optimised for fast and reliable numerical evaluation in the physical region.