Enhancement of B (B_{d}→μ^{+}μ^{-})/B (B_{s}→μ^{+}μ^{-}) in the MSSM with modified minimal flavor violation and large tan β

We extend our previous analysis of the decays B_{d,s} -> mu^+ mu^- in the Minimal Supersymmetric Standard Model (MSSM) to include gluino and neutralino contributions. We provide analytic formulae, 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^{+/-}, H^{+/-}, charginos), and assuming the Cabibbo-Kobayashi-Maskawa (CKM) matrix to be the only source of flavour violation, we assess their implications for the branching fractions Br(B_{d,s} -> mu^+ mu^-). Of particular interest is the quantity R = Br(B_d -> mu^+ mu^-)/Br(B_s -> 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_{td}/V_{ts}| in the Standard Model (SM), which predicts R_SM ~ |V_{td}/V_{ts}|^2 ~ O(10^{-2}). Exploring three different scenarios of modified minimal flavour violation, we find that part of the MSSM parameter space can accommodate large Br(B_{d,s} -> 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(1), 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} -> mu^+ mu^- and B_{s} -> mu^+ mu^- can be of comparable size even in the case where flavour violation is due solely to the CKM matrix.