Two-loop light fermion contribution to Higgs production and decays

We compute the electroweak corrections due to the light fermions to the production cross section $\sigma(g g \to H)$ and to the partial decay widths $\Gamma (H \to \gamma \gamma)$ and $\Gamma (H \to g g)$. We present analytic results for these corrections that are expressed in terms of Generalized Harmonic Polylogarithms. We find that for the gluon fusion production cross section and for the decay width $\Gamma (H \to g g)$ the corrections are large in the Higgs mass region below 160 GeV where they reach up to 9% of the lowest order term. For the decay width $\Gamma (H \to \gamma \gamma)$ the corrections for Higgs mass above 160 GeV can reach $-$10% of the lowest order term.