The rare decay b→sg beyond leading logarithms

We calculate the O(αs) virtual corrections to the decay width for b→sg in the standard model (g denotes a gluon). Also the corresponding O(αs) bremsstrahlung corrections to b→sg are systematically calculated in this Letter. The combined result is free of infrared and collinear singularities, in accordance with the KLN theorem. Taking into account the existing next-to-leading logarithmic (NLL) result for the Wilson coefficient C8eff, a complete NLL result for the branching ratio BNLL(b→sg) is derived. Numerically, we obtain BNLL=(5.0±1.0)×10−3, which is more than a factor of two larger than the leading logarithmic result BLL=(2.2±0.8)×10−3.