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We explore the parameter space of the type-II two-Higgs-doublet model withsoftly broken Z2 symmetry, allowing for CP violation in the scalar potential.Imposing theory-motivated and experimentally-driven constraints, we show thatas the CP-violating phases are increased, only small regions of parameter spacesurvive, including regions slightly away from the alignment limit. Electroweakoblique parameters and electric dipole moments emerge as most restrictiveconstraints. We show that imposing these constraints (as well as theoreticalbounds such as perturbativity) the masses of the charged and heavy neutralHiggs, unlike in the CP conserving case, are bound from above and below. Inparticular, the heavy neutral Higgs masses are almost degenerate. In thisparameter space region we highlight the relevant decay signals of the heavyneutral Higgs, involving both Zh and WW=ZZ, indicative of CP violation in themodel.

Restricting the parameter space of Type-II Two Higgs Doublet Models with CP violation