Minimal flavor violations and tree level flavor changing neutral currents

Abstract

Consequences of a specific class of two Higgs doublet models in which the Higgs induced tree level flavor changing neutral currents (FCNC) display minimal flavor violation are considered. These FCNC are fixed in terms of the Cabibbo Kobayashi Maskawa (CKM) matrix elements and the down quark masses. The minimal model in this category with only two Higgs doublets has no extra $CP$ violating phases, but such a phase can be induced by adding a complex singlet Higgs. The FCNC contribute significantly to $B$ meson mixing and $CP$ violation, but similar contributions in case of the $K$ mesons are suppressed. Detailed numerical analysis to determine the allowed Higgs contributions to neutral meson mixings and the CKM parameters $\overline{\ensuremath{\rho}}$, $\overline{\ensuremath{\eta}}$ in their presence is presented. The Higgs induced phase in the ${B}_{d,s}^{0}\ensuremath{-}{\overline{B}}_{d,s}^{0}$ transition amplitude ${M}_{12}^{d,s}$ is predicted to be equal for the ${B}_{d}$ and the ${B}_{s}$ systems. There is a strong correlation between $|{V}_{ub}|$ and phases ${\ensuremath{\phi}}_{d,s}$ in ${M}_{12}^{d,s}$. A measurable $CP$ violating phase ${\ensuremath{\phi}}_{s}=\ensuremath{-}0.18\ifmmode\pm\else\textpm\fi{}0.08$ is predicted on the basis of the observed phase ${\ensuremath{\phi}}_{d}$ in the ${B}_{d}$ system if $|{V}_{ub}|$ is large and close to its value determined from the inclusive $b$ decays.