# The light-fermion contribution to the exact Higgs-gluon form factor in QCD

## TL;DR

This paper derives an exact three-loop analytical expression for the Higgs-gluon form factor involving light quark loops in QCD, confirming previous approximations and expanding understanding of Higgs interactions.

## Contribution

It provides the first complete analytical formula for the three-loop light-fermion contribution to the Higgs-gluon form factor in QCD, expressed with harmonic polylogarithms.

## Key findings

- The analytical expression agrees with previous kinematic expansions.
- It confirms the accuracy of recent semi-numerical approximations.
- The result extends the understanding of Higgs interactions in QCD.

## Abstract

An analytical expression for the three-loop form factors for $ggH$ and $\gamma\gamma H$ is derived for the contributions which involve massless quark loops. The result is expressed in terms of harmonic polylogarithms. It fully agrees with previously obtained kinematical expansions, and confirms a recent semi-numerical approximation which extends over the full kinematic range.