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

Abstract

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 ${\bar{B}}_s\to {\mu }^{+}{\mu }^{-}$ and ${\bar{B}}_d\to \bar{K}{\mu }^{+}{\mu }^{-}$ numerically by considering general variations in the Higgs parameters assuming that Higgs sector conserves CP. Taking the results on $B_s^0-{\bar{B}}_s^0$ mixing derived by the global analysis of UTfit group as a guide we present the general constraints on $F_{23}^{\ast }{F}_{32}$ in terms of the pseudo-scalar mass $M_A$. The former is required to be in the range $\sim (1-5)\times 10^{-11}{M}_A^2{\mathrm{GeV}}^{-2}$ 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 $B_s^0-{\bar{B}}_s^0$ mixing except when $F_{23}=F_{32}$. The Higgs contribution to ${\bar{B}}_s\to {\mu }^{+}{\mu }^{-}$ branching ratio can be large, close to the present limit while it remains close to the standard model value in case of the process ${\bar{B}}_d\to \bar{K}{\mu }^{+}{\mu }^{-}$ for all the models under study. We identify and discuss various specific examples which can naturally lead to suppressed FCNC in the $K^0-{\bar{K}}^0$ mixing allowing at the same time the required values for $F_{23}^{\ast }$ and $F_{32}$.

Comments: 19 pages;six figures