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

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.