Two-loop electroweak corrections to the Higgs-boson decay $H \to \gamma \gamma$

The complete set of two-loop electroweak corrections to the decay width of the Higgs boson into two photons is presented. Two-loop contributions involving weak bosons and the top quark are computed in terms of an expansion in the Higgs external momentum. Adding these results to the previously known light fermion contributions, we find that the total electroweak corrections for a Higgs boson with 100 GeV <m_H < 150 GeV are moderate and negative, between -4% < delta_EW < 0%. Combination with the QCD corrections, which are small and positive, gives a total correction to the one-loop results of | delta_{EW+QCD}|< 1.5 %.