The experimental study of $B$ mesons suggest the existence of some new physics contribution to the $B_s^0-{\overline{B}}_s^0$ mixing. We study the implications of a hypothesis that this contribution is generated by the Higgs-induced flavor-changing neutral currents (FCNC). We concentrate on the specific $b\to s$ transition which is described by two complex FCNC parameters, $F_{23}$ and $F_{32}$, and parameters in the Higgs sector. Model-independent constraints on these parameters are derived from the $B_s^0-{\overline{B}}_s^0$ mixing and are used to predict the branching ratios for ${\overline{B}}_s\to {\mu }^{+}{\mu }^{-}$ and ${\overline{B}}_d\to \overline{K}{\mu }^{+}{\mu }^{-}$ numerically by considering general variations in the Higgs parameters assuming that Higgs sector conserves $CP$. Taking the results on $B_s^0-{\overline{B}}_s^0$ mixing derived by the global analysis of UTfit group as a guide we present the general constraints on $F_{23}^{*}{F}_{32}$ in terms of the pseudoscalar mass $M_A$. The former is required to be in the range $\sim (1–5)\times {10}^{-11}{M}_A^2{\mathrm{GeV}}^{-2}$ if the Higgs-induced FCNC represent the dominant source of new physics. The phases of these couplings can account for the large $CP$ violating phase in the $B_s^0-{\overline{B}}_s^0$ mixing except when $F_{23}=F_{32}$. The Higgs contribution to ${\overline{B}}_s\to {\mu }^{+}{\mu }^{-}$ branching ratio can be large, close to the present limit while it remains close to the standard model value in case of the process ${\overline{B}}_d\to \overline{K}{\mu }^{+}{\mu }^{-}$ for all the models under study. We identify and discuss various specific examples which can naturally lead to suppressed FCNC in the $K^0-{\overline{K}}^0$ mixing allowing at the same time the required values for $F_{23}^{*}$ and $F_{32}$.

• Received 31 October 2009

DOI:https://doi.org/10.1103/PhysRevD.81.035013