Higgs-Mediated $B^0 -> \mu^+ \mu^-$ in Minimal Supersymmetry

In this letter we demonstrate a new source for large flavor-changing neutral currents within the minimal supersymmetric standard model. At moderate to large tan(beta), it is no longer possible to diagonalize the masses of the quarks in the same basis as their Yukawa couplings. This generates large flavor-violating couplings of the form $\bar b_R d_L H$ and $\bar b_R s_L H$ where H is any of the three neutral, physical Higgs bosons. These new couplings lead to rare processes in the B system such as $B^0 -> \mu^+ \mu^-$ decay and B-Bbar mixing. We show that the latter is anomalously suppressed, while the former is in the experimentally interesting range. Current limits on $B^0 -> \mu^+ \mu^-$ already provide nontrivial constraints on models of moderate to large tan(beta), with an observable signal possible at Run II of the Tevatron if m_A < 400-600 GeV, extending to the TeV range if a proposed Run III of 30/fb were to occur.