Enhancement ofB(Bd→μ+μ−)/B(Bs→μ+μ−)in the MSSM with modified minimal flavor violation and largetanβ

We extend our previous analysis of the decays $B_{d,s}\to {\mu }^{+}{\mu }^{-}$ in the minimal supersymmetric standard model (MSSM) to include gluino and neutralino contributions. We provide analytic formulas, valid at large values of $\tan \beta ,$ for the scalar and pseudoscalar Wilson coefficients arising from neutral Higgs boson exchange diagrams with gluinos and neutralinos. Together with the remaining contributions ${(W}^{\pm },$ $H^{\pm },$ ${\tilde{\chi }}^{\pm }),$ and assuming the Cabibbo-Kobayashi-Maskawa (CKM) matrix to be the only source of flavor violation, we assess their implications for the branching fractions $\mathcal{B}(B_{d,s}\to {\mu }^{+}{\mu }^{-}).\mathrm{}$ Of particular interest is the quantity $R\equiv \mathcal{B}(B_d\to {\mu }^{+}{\mu }^{-})/\mathcal{B}(B_s\to {\mu }^{+}{\mu }^{-}),$ since (i) the theoretical errors cancel to a large extent, and (ii) it offers a theoretically clean way of extracting the ratio $|V_{\mathrm{td}}{/V}_{\mathrm{ts}}|$ in the standard model, which predicts $R_{\mathrm{SM}}\sim |V_{\mathrm{td}}{/V}_{\mathrm{ts}}{|}^2\sim {O(10\mathrm{}}^{-2}).\mathrm{}$ Exploring three different scenarios of modified minimal flavor violation $\left(\overline{\mathrm{MFV}}\right),$ we find that part of the MSSM parameter space can accommodate large $B_{d,s}\to {\mu }^{+}{\mu }^{-}$ branching fractions while being consistent with various experimental constraints. More importantly, we show that the ratio R can be as large as $O\left(1\right),$ while the individual branching fractions may be amenable to detection by ongoing experiments. We conclude that within the MSSM with large $\tan \beta$ the decay rates of $B_d\to {\mu }^{+}{\mu }^{-}$ and $B_s\to {\mu }^{+}{\mu }^{-}$ can be of comparable size even in the case where flavor violation is due solely to the CKM matrix.