Complete electroweak matching for radiative b decays

Abstract

We compute the complete two-loop O(α) Wilson coefficients relevant for radiative decays of the B meson in the SM. This is a necessary step in the calculation of the O(ααsn lnn mb /MW ) corrections and improves on our previous analysis of electroweak effects in B → Xs γ. We describe in detail several interesting technical aspects of the calculation and include all dominant QED matrix elements. In our final result, we neglect only terms originated from the unknown O(ααs ) evolution of the Wilson coefficients and some suppressed two-loop matrix elements. Due to the compensation among different effects, we find that non-trivial electroweak corrections decrease the branching ratio by about 3.6% for a light Higgs boson, very close to our previous result. The corresponding SM prediction for the branching ratio with Eγ > 1.6 GeV is (3.61 ± 0.30) × 10−4 .