Electroweak effects in radiative B decays

We compute the two-loop electroweak corrections to the radiative decays of the B meson in the SM. Electroweak effects reduce the Wilson coefficient C7eff (Mw) by 2.6% for a light Higgs boson of about 100 GeV and are less important for a heavier Higgs. The leading term of a heavy top expansion of our result differs from the one obtained in the gaugeless approximation where only top quark Yukawa couplings are considered: we discuss the origin of the discrepancy and provide a criterion for the validity of the gaugeless approximation. As a byproduct of the calculation we also obtain the O(α) corrections to the Wilson coefficient of the four-fermion operator Q2. A careful analysis of the interplay between electroweak and QCD effects leads to an overall 2% reduction of the total branching ratio for B → Xsγ due to purely electroweak corrections. For a light Higgs boson, the up-to-date SM prediction is BRγ = (3.29 ± 0.21) × 10-4