Flavor and CP-violating Higgs sector in two Higgs doublet models with $U(1)'$

Abstract

We investigate the role of a local $U(1)'$ symmetry for the problem of CP violation in the effective theory for two Higgs doublet models and its microscopic counterparts. First, in two Higgs doublet models with $U(1)'$, we show that the higher-dimensional operators in the scalar potential violate the CP symmetry with an interplay with the mixing mass parameter, giving rise to small mixings between CP-even and CP-odd scalars. Motivated by the $B$-meson anomalies in recent years, we take the flavored $U(1)'$ to be a benchmark model for specifying the flavor structure. Then, we calculate the electric dipole moment of electron (eEDM) at two loops due to the CP-violating higher-dimensional operators and identify the correlation between the masses of heavy Higgs bosons and the cutoff scale from the bound on eEDM. We also comment on the possibility of making an independent test of the CP violation in the collider searches for heavy Higgs bosons. Finally, we show how the obtained eEDM results in the effective theory can be used to constrain microscopic models with an explicit CP violation in the partially decoupled or dark sectors.