We study $\mathrm{CP}$ violation in a multi-Higgs-doublet model based on a $S_3\times Z_3$ horizontal symmetry where the CKM phase is not the principal source of $\mathrm{CP}$ violation. We consider two mechanisms for $\mathrm{CP}$ violation in this model: (a) $\mathrm{CP}$ violation due to complex Yukawa couplings, and (b) $\mathrm{CP}$ violation due to scalar-pseudoscalar Higgs boson mixings. Both mechanisms can explain the observed $\mathrm{CP}$ violation in the neutral kaon system. $\frac{{\epsilon }^{\prime }}{\epsilon }$ due to neutral Higgs boson exchange is small in both mechanisms, but charged Higgs boson contributions can be as large as ${10}^{-4\mathrm{}}$ for (a), and ${10}^{-3\mathrm{}}$ for (b). $\mathrm{CP}$ violation in the neutral $B$ system is, however, quite different from the minimal standard model. The neutron electric dipole moment can be as large as the present experimental bound, and can be used to constrain charged Higgs boson masses. The electron EDM is one order of magnitude below the experimental bound in case (b) and smaller in case (a).

• Received 10 December 1993

DOI:https://doi.org/10.1103/PhysRevD.49.4812