Correlating the Higgs and Kaon Sector CP Violations

Taking the most general two-doublet models with explicit CP violation in the Higgs sector but no phase in the CKM matrix, we determine the correlation between the Higgs and Kaon sectors using the experimental values of $\Delta M_K$ and $\epsilon_K$. It is found that: there is a direct correlation between strength of FCNC couplings and the Higgs masses, and the lightest Higgs is nearly pure CP-even, but this small CP-odd composition gives large enough contribution to $\epsilon_K$.