CP violation in models with two- and three-scalar doublets

We reanalyze the two- and three-scalar (Higgs) doublet models with spontaneous CP violation. We show that the two-Higgs doublet model of T.D. Lee can be made consistent with the recent measurements of ε{lunate}′/ε{lunate} provided the ΔS = 2 amplitudes receive important contributions from neutral Higgs exchanges. The sign of ε{lunate}′/ε{lunate} is positive in this model. The main part of our paper constitutes a new calculation of CP violation in the three-Higgs doublet model with natural flavor conservation. We find in contrast to previous analyses that this model is consistent with the experimental value of ε{lunate}′/ε{lunate} provided an interesting hierarchy among the vacuum expectation values present in the model is assumed. ε{lunate}′/ε{lunate} can have both signs in this model and is typically ±0.005. Simultaneously ΔM(K₁ - K_s), the ε{lunate}-parameter and the electric dipole moment of the neutron are consistent with the experimental data.