Intrinsic properties of large C P violation in the complex two-Higgs-doublet model

We investigate the parameter space supporting large C P violation (CPV) in the complex two-Higgs-doublet model with softly broken Z 2 symmetry, where the 125 GeV Higgs boson is identified as the lightest neutral Higgs boson H 1 . Through a comprehensive global scan of type-I and type-II models under theoretical, collider, and eEDM constraints, we identify distinct structures that facilitate large CPV. In type-I, gauge-sector CPV is maximized when the 125 GeV Higgs boson is nearly degenerate with a second neutral scalar. For the ensemble of physically viable points, the predicted eEDM values typically exceed 10 − 31 e cm , placing the model largely within the sensitivity of next-generation experiments. Conversely, type-II models strongly suppress gauge-sector CPV while allowing for nearly maximal CPV in the Yukawa sector. Destructive interference among various contributions allows for | d e | values as low as O ( 10 − 35 ) e cm , resulting in no phenomenologically relevant lower bound. Finally, we uncover the phenomenon of “hidden CPV” in the near-alignment limit, characterized by C P -violating mixing between the heavy neutral Higgs bosons governed by the angle α 3 . We demonstrate that this hidden CPV can be experimentally probed at future colliders via C P -violating Yukawa interactions of H 2 and H 3 , as well as the robust H 2 − H 3 − Z coupling.