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Abstract

We report on a calculation of Higgs-boson contributions to the decays ${B}_{s}\ensuremath{\rightarrow}{l}^{+}{l}^{\ensuremath{-}}$ and $\overline{B}\ensuremath{\rightarrow}{\mathrm{Kl}}^{+}{l}^{\ensuremath{-}}$ $(l=e,\ensuremath{\mu})$ which are governed by the effective Hamiltonian describing $\stackrel{\ensuremath{\rightarrow}}{b}{\mathrm{sl}}^{+}{l}^{\ensuremath{-}}.$ Compact formulas for the Wilson coefficients are provided in the context of the type-II two-Higgs-doublet model (2HDM) and supersymmetry (SUSY) with minimal flavor violation, focusing on the case of large $\mathrm{tan}\ensuremath{\beta}.$ We derive, in a model-independent way, constraints on Higgs-boson-mediated interactions, using present experimental results on rare B decays including $\stackrel{\ensuremath{\rightarrow}}{b}s\ensuremath{\gamma},$ ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}},$ and $\overline{B}\ensuremath{\rightarrow}{K}^{(*)}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}.$ In particular, we assess the impact of possible scalar and pseudoscalar interactions transcending the standard model (SM) on the branching ratio of ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ and the forward-backward (FB) asymmetry of ${\ensuremath{\mu}}^{\ensuremath{-}}$ in $\overline{B}\ensuremath{\rightarrow}K{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ 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 $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}.$ Moreover, striking effects on the decay spectrum of $\overline{B}\ensuremath{\rightarrow}K{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ are already ruled out by experimental data on the ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ 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 $\stackrel{\ensuremath{\rightarrow}}{b}s\ensuremath{\gamma}$ can significantly affect the branching ratio of ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}.$ We also comment on previous calculations contained in the literature.