New Higgs Effects in B--Physics in Supersymmetry with General Flavour Mixing

Abstract

We investigate the effect of general flavour mixing among squarks on the rare decays $\bar{B}\to X_s\gamma$, ${\bar{B}}_s\to {\mu }^{+}{\mu }^{-}$ and ${\bar{B}}_s-B_s$ mixing beyond the leading order in perturbation theory. We include all large $\tan \beta$--enhanced corrections whilst also taking into account the effects of general flavour mixing on the uncorrected quark mass matrix and $\mathrm{SU}(2{)}_L\times \mathrm{U}(1{)}_Y$ breaking. For ${\bar{B}}_s\to {\mu }^{+}{\mu }^{-}$ and ${\bar{B}}_s-B_s$ mixing we find that, in analogy to $\bar{B}\to X_s\gamma$, there appears a focusing effect which can reduce the contribution due to the ${\delta }_{RR}$ (and the ${\delta }_{LL}$) insertion by up to a factor of two at large $\tan \beta$ and $\mu >0$. A dependence on ${\delta }_{LR}$ and ${\delta }_{RL}$, that otherwise cancels to first order in the mass insertion approximation, is also reintroduced. Taking into account the current experimental bounds on $\Delta M_{B_s}$ and BR(${\bar{B}}_s\to {\mu }^{+}{\mu }^{-}$), we find that the insertions ${\delta }_{RL}$ and ${\delta }_{RR}$ can be significantly constrained compared to bounds obtained from $\bar{B}\to X_s\gamma$ only.

arXiv commentversion to appear in PLB, minor corrections

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