We report on a calculation of Higgs-boson contributions to the decays and (B) over bar (s)-->l(+)l(-) and (B) over bar --> Kl(+)l(-) (l = e,mu) which are governed by the effective Hamiltonian describing b --> sl(+)l(-). Compact formulas for the Wilson coefficients are provided in the context of the type-II two-Hi.-gs-doublet model (2HDM) and supersymmetry (SUSY) with minimal flavor violation, focusing on the case of large tan beta. We derive, in a model-independent way, constraints on Higgs-boson-mediated interactions, using present experimental results on rare B decays including b-s gamma, (B) over bar (s)--> mu (+)mu (-), and (B) over barK((*))mu (+)mu (-). In particular, we assess the impact of possible scalar and pseudoscalar interactions transcending the standard model (SM) on the branching ratio of (B) over bar (s)--> mu (+)mu (-) and the forward-backward (FB) asymmetry of mu (-) in (B) over bar -->K mu (+)mu (-) decay. The average FB asymmetry, which is unobservably small within the SM, and therefore a potentially valuable tool to search for new physics, is predicted to be no greater than 4% for a nominal branching ratio of about 6 x 10(-7). Moreover, striking effects on the decay spectrum of (B) over bar -->K mu (+)mu (-) are already ruled out by experimental data on the (B) over bar (s)--> mu (+)mu (-) branching fraction. In addition, we study the constraints on the parameter space of the 2HDM and SUSY with minimal flavor violation. While the type-II 2HDM does not give any sizable contributions to the above decay modes, we find that SUSY contributions obeying the constraint on b -->s gamma can significantly affect the branching ratio of (B) over bar (s)--> mu (+)mu (-). We also comment on previous calculations contained in the literature.
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