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.
Categories: hep-ph