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Higgs-mediated leptonic decays of B_s and B_d mesons as probes of supersymmetry

If tan(beta) is large, down-type quark mass matrices and Yukawa couplings cannot be simultaneously diagonalized, and flavour violating couplings of the neutral Higgs bosons are induced at the 1-loop level. These couplings lead to Higgs-mediated contributions to the decays B_s -> mu+ mu- and B_d -> tau+ tau-, at a level that might be of interest for the current Tevatron run, or possibly, at B-factories. We evaluate the branching ratios for these decays within the framework of minimal gravity-, gauge- and anomaly-mediated SUSY breaking models, and also in SU(5) supergravity models with non-universal gaugino mass parameters at the GUT scale. We find that the contribution from gluino loops, which seems to have been left out in recent phenomenological analyses, is significant. We explore how the branching fraction varies in these models, emphasizing parameter regions consistent with other observations.