Minimal flavour violations and tree level FCNC

Consequences of a specific class of two Higgs doublet models in which the Higgs induced tree level flavour changing neutral currents (FCNC) display minimal flavour violation (MFV) are considered. These FCNC are fixed in terms of the 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. Many of the theoretical predictions are similar to other MFV scenario. The FCNC contribute significantly to $B$ meson mixing and CP violation. Detailed numerical analysis to determine the allowed Higgs contributions to neutral meson mixings and the CKM parameters $\bar{\rho},\bar{\eta}$ in their presence is presented. The Higgs induced phase in the $B^0_{d,s}-\bar{B}^0_{d,s}$ 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 phases in $M_{12}^{d,s}$ and $|V_{ub}|$. A measurable CP violating phase $\phi_s=-0.18\pm 0.08$ is predicted on the basis of the observed phase $\phi_d$ in the $B_d$ system if $|V_{ub}|$ is large and close to its value determined from the inclusive b decays.