Minimal flavor violations and tree level flavor changing neutral currents

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 ρ, η in their presence is presented. The Higgs induced phase in the Bd,s0-Bd,s0 transition amplitude M12d,s is predicted to be equal for the Bd and the Bs systems. There is a strong correlation between |Vub| and phases φd,s in M12d,s. A measurable CP violating phase φs=-0.18±0.08 is predicted on the basis of the observed phase φd in the Bd system if |Vub| is large and close to its value determined from the inclusive b decays.