We undertake a systematic study of the interplay between Higgs alignment and CP-violation, which enables us to identify a scenario where departures from Higgs alignment could be present independently of CP-violation. After including constraints from the electric dipole moment and measurements at the Large Hadron Collider, we suggest a smoking-gun signal of CP-violation in the Higgs-to-Higgs decay. The mere presence of this decay channel is sufficient to establish CP-violation in a complex two-Higgs-doublet model. A distinct discovery channel lies in final states with three 125 GeV Higgs bosons, which has yet to be searched for, and could be detected at the high-luminosity LHC.
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With support from FCT through project UIDB/00777/2020
