Virtual corrections to the decay b → s + γ

We calculate the O(αs) virtual corrections to the matrix element for b → sγ, taking into account the contributions of the four-Fermi operator O2 and the electromagnetic and color dipole-type operators. The results are combined with existing O(αs) Bremsstrahlung corrections in order to obtain the relevant inclusive rate. The new result drastically reduces the large scale dependence of the leading logarithmic approximation. It implies that a very accurate prediction for the branching ratio for B → Xsγ will become possible once also the corrections to the Wilson coefficients are available.