Bd,s0→μ−μ+decay in the MSSM

We present the results of the complete one-loop computation of the $B_{d,s}^0\to l^{+}{l}^{-}$ decay rate in the MSSM. Both sources of the FCNC, the CKM matrix and off-diagonal entries of the sfermion mass matrices are considered. Strong enhancement of the branching ratio (compared to the SM prediction) can be obtained in the large $\tan \beta \sim m_t{/m}_b$ regime in which the neutral Higgs boson “penguin” diagrams dominate. We make explicit the strong dependence of this enhancement on the top squarks mixing angle in the case of the chargino contribution and on the $\mu$ parameter in the case of the gluino contribution. We show that, in some regions of the MSSM parameter space, the branching ratio for this process can be as large as ${10}^{-\left(5\mathrm{}-4\right)}$ respecting all existing constraints, including the CLEO measurement of $\mathrm{BR}\left(\overrightarrow{B}{X}_s\gamma \right).\mathrm{}$ We also estimate that for chargino and top squark masses $\sim \mathcal{O}(100\mathrm{}$ GeV) $\mathrm{BR}{(B}_s^0\to l^{+}{l}^{{}^{\prime }-})$ with ${\mathrm{ll}}^{\prime }=e\tau$ or $\mu \tau$ can be of the order of ${10}^{-11}$ for the still allowed values of the off-diagonal entries in the slepton mass matrix.