Two-loop electroweak corrections to Higgs-gluon couplings to higher orders in the dimensional regularization parameter

TL;DR

This paper calculates two-loop electroweak corrections to Higgs production via gluon fusion, advancing precision in theoretical predictions by employing differential equations and Goncharov polylogarithms.

Contribution

It introduces a method to compute higher-order electroweak corrections using differential equations and polylogarithms, essential for three-loop mixed QCD-electroweak calculations.

Findings

Computed two-loop electroweak corrections to Higgs-gluon coupling.

Expressed integrals in terms of Goncharov polylogarithms.

Provides inputs for future three-loop correction calculations.

Abstract

We compute the two-loop electroweak correction to the production of the Higgs boson in gluon fusion to higher orders in the dimensional-regularization parameter $\epsilon = (d-4)/2$. We employ the method of differential equations to compute the relevant integrals and express them in terms of Goncharov polylogarithms. Our result provides one of the necessary inputs for the computation of mixed three-loop QCD-electroweak corrections to $gg \to H$.