Complete next-to-leading order gluino contributions to [formula omitted] and [formula omitted

Abstract

We present the first complete order α s corrections to the Wilson coefficients (at the high scale) of the various versions of magnetic and chromomagnetic operators which are induced by a squark–gluino exchange. For this matching calculation, we work out the on-shell amplitudes b → s γ and b → s g , both in the full and in the effective theory up to order α s 2 . The most difficult part of the calculation is the evaluation of the two-loop diagrams in the full theory; these can be split into two classes: a) diagrams with one gluino and a virtual gluon; b) diagrams with two gluinos or with one gluino and a four-squark vertex. Accordingly, the Wilson coefficients can be split into a part a) and a part b). While part b) of the Wilson coefficients is presented in this paper for the first time, part a) was given in Bobeth et al. (2000) [1]. We checked their results for the coefficients of the magnetic operators and found perfect agreement. Moreover, we work out the renormalization procedure in great detail. Our results for the complete next-to-leading order Wilson coefficients are fully analytic, but far too long to be printed. We therefore publish them in the form of a C++ program. They constitute a crucial building block for the phenomenological next-to-leading logarithmic analysis of the branching ratio B ¯ → X s γ in a supersymmetric model beyond minimal flavor violation.