Analysis of neutral Higgs-boson contributions to the decays $B_s\to l^{+}{l}^{-}$ and $\overline{B}\to {\mathrm{Kl}}^{+}{l}^{-}$

We report on a calculation of Higgs-boson contributions to the decays $B_s\to l^{+}{l}^{-}$ and $\overline{B}\to {\mathrm{Kl}}^{+}{l}^{-}$ $(l=e,\mu )$ which are governed by the effective Hamiltonian describing $\overrightarrow{b}{\mathrm{sl}}^{+}{l}^{-}.$ 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 $\tan \beta .$ We derive, in a model-independent way, constraints on Higgs-boson-mediated interactions, using present experimental results on rare B decays including $\overrightarrow{b}s\gamma ,$ $B_s\to {\mu }^{+}{\mu }^{-},$ and $\overline{B}\to K^{\left(*\right)}{\mu }^{+}{\mu }^{-}.$ In particular, we assess the impact of possible scalar and pseudoscalar interactions transcending the standard model (SM) on the branching ratio of $B_s\to {\mu }^{+}{\mu }^{-}$ and the forward-backward (FB) asymmetry of ${\mu }^{-}$ in $\overline{B}\to K{\mu }^{+}{\mu }^{-}$ 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 $6\times {10}^{-7}.$ Moreover, striking effects on the decay spectrum of $\overline{B}\to K{\mu }^{+}{\mu }^{-}$ are already ruled out by experimental data on the $B_s\to {\mu }^{+}{\mu }^{-}$ 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 $\overrightarrow{b}s\gamma$ can significantly affect the branching ratio of $B_s\to {\mu }^{+}{\mu }^{-}.$ We also comment on previous calculations contained in the literature.