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

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 ${\rm SU}(2)_L\times{\rm U}(1)_Y$ 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.