Electroweak effects in radiative B decays

We compute the two-loop electroweak corrections to the radiative decays ofthe B meson in the SM. Electroweak effects reduce the Wilson coefficientC_7^eff(mw) by 2.6% for a light Higgs boson of about 100 GeV and are lessimportant for a heavier Higgs. The leading term of a heavy top expansion of ourresult differs from the one obtained in the gaugeless approximation where onlytop quark Yukawa couplings are considered: we discuss the origin of thediscrepancy and provide a criterion for the validity of the gaugelessapproximation. As a byproduct of the calculation we also obtain the O(alpha)corrections to the Wilson coefficient of the four-fermion operator Q_2. Acareful analysis of the interplay between electroweak and QCD effects leads toan overall 2% reduction of the total branching ratio for B -> X_s gamma due topurely electroweak corrections. For a light Higgs boson, the up-to-date SMprediction is BR_gamma=3.29 10^-4.Comment: 15 pages, 3 figure