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Complete next-to-leading order gluino contributions to \(b\rightarrow s\gamma\) and \(b\rightarrow sg\). (English) Zbl 1229.81306

Summary: We present the first complete order \(\alpha_s\) 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 \(b\rightarrow s\gamma \) and \(b\rightarrow sg\), both in the full and in the effective theory up to order \(\alpha_s^2\). 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). 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 \(\bar{B}\rightarrow X_s\gamma\) in a supersymmetric model beyond minimal flavor violation.

MSC:

81V05 Strong interaction, including quantum chromodynamics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory

Software:

bsg2gluino
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References:

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