Probing the Flavour Structure of Supersymmetry Breaking With Rare B-Processes - A Beyond Leading Order Analysis

Abstract

In the framework of minimal supersymmetry with general flavour mixing in the squark sector we consider dominant beyond leading order (BLO) effects in the rare processes $\bar{B}\to X_s\gamma$, ${\bar{B}}_s{\mu }^{+}{\mu }^{-}$ and ${\bar{B}}_s-B_s$ mixing. We present analytic expressions for corrected vertices, which are applicable in general, and provide a recipe for the inclusion of the dominant and subdominant BLO effects in existing LO calculations. We also derive similar expressions in the mass insertion approximation. We investigate in more detail the focusing effect pointed out in our earlier work, which, at large $\tan \beta$ and $\mu >0$, leads to a reduced supersymmetric contribution to the above processes. We also find that, in some cases, flavour dependence, that accidentally cancels at leading order, can reappear at BLO. We further include electroweak corrections, which, while generally subdominant, in some cases may have a substantial effect. For example, their contribution to the charged Higgs vertex in $\bar{B}\to X_s\gamma$ can be of the order of 20% at BLO. They can also reduce the contribution of LL insertions to ${\bar{B}}_s\to {\mu }^{+}{\mu }^{-}$ and ${\bar{B}}_s-B_s$ mixing by up to 20%, even at the LO. We also analyse radiative generation of CKM elements and find the possibility that the CKM matrix elements $K_{ts}$ and $K_{cb}$ can be generated entirely by LR insertions. This work constitutes the first complete analysis of dominant BLO effects in the GFM scenario.

74 pages

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