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Higgs induced FCNC as a source of new physics in $b\to s $ transitions

The observations in the $B_{s}$ sector suggest the existence of some new physics contribution to the $B_S-\bar{B}_s$ mixing. We study the implications of a hypothesis that this contribution is generated by the Higgs induced flavour changing neutral currents. 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 $B_S-\bar{B}_s$ mixing and are used to predict the branching ratios for $\bar{B}_s\to μ^+μ^-$ and $\bar{B}_d\to \bar{K}μ^+μ^-$ numerically by considering general variations in the Higgs parameters assuming that Higgs sector conserves CP. Taking the results on $B_{s}^0-\bar{B}_{s}^0$ 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 pseudo-scalar mass $M_A$. The former is required to be in the range $\sim (1-5) \times 10^{-11} M_A^2 {\rm GeV}^{-2}$ 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 $B_{s}^0-\bar{B}_{s}^0$ mixing except when $F_{23}=F_{32}$. The Higgs contribution to $\bar{B}_s\to μ^+μ^-$ branching ratio can be large, close to the present limit while it remains close to the standard model value in case of the process $\bar{B}_d\to \bar{K}μ^+μ^-$ for all the models under study. We identify and discuss various specific examples which can naturally lead to suppressed FCNC in the $K^0-\bar{K}^0$ mixing allowing at the same time the required values for $F_{23}^*$ and $F_{32}$.