Three-loop matching of the dipole operators for b → sγ and b → sg

We evaluate the three-loop matching conditions for the dimension-five operators that are relevant for the b --> sgamma decay. Our calculation completes the first out of three steps (matching, mixing and matrix elements) that are necessary for finding the next-to-next-to-leading QCD corrections to this process. All such corrections must be calculated in view of the ongoing accurate measurements of the (B) over bar --> X(s)gamma branching ratio. (C) 2004 Elsevier B.V. All rights reserved.