Spontaneous CP-Violation in the Extended Standard Models

The spontaneous CP-violation in three kinds of extension of the standard model are investigated. We find that if no additional symmetry is introduced to reduce the number of coefficients, then all three extended models possess the spontaneous CP violation (SCPV) in the Higgs potential. When symmetry under which the doublets transform as $Φ_1 \to Φ_1$ and $Φ_2 \to e^{iγ}Φ_2$ is introduced, the two-Higgs doublet model will lose its SCPV terms. In the other two extended models, the SCPV terms will be preserved since both models contain at least one Higgs singlet which can appear in odd powers. The extended model with two doublets and one singlet is reviewed and the general conditions which make the CP-violating $V_{min}$ the true minimum are given. The generally called natural flavour-conserving models are also discussed briefly.

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