Complete next-to-leading order gluino contributions to b--> s gamma and b--> s g

TL;DR

This paper provides the first complete next-to-leading order calculations of gluino contributions to b--> s gamma and b--> s g processes, crucial for precise supersymmetric phenomenology.

Contribution

It introduces the full analytic NLO Wilson coefficients for gluino-induced operators, including new two-loop diagram evaluations and a detailed renormalization procedure.

Findings

Complete NLO Wilson coefficients published as a C++ program

First calculation of two-gluino and four-squark vertex diagrams at this order

Results enable more accurate supersymmetric B decay predictions

Abstract

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--> s gamma and b --> s g, 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.). 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 Bbar --> X_s gamma in a supersymmetric model beyond minimal flavor violation.