Higgs alignment and novel CP-violating observables in 2HDM

We propose novel CP-violating observables in complex two-Higgs-doublet models and undertake a systematic study of the interplay between Higgs alignment and CP-violation, which enables us to distinguish two separate sources of CP-violation in the scalar sector: in the mixing and in the decay, and 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, without recourse to the typically required angular correlations, in the Higgs-to-Higgs decay, $(h_3\to h_2 h_1)$, where $h_3, h_2$, and $h_1$ are the heaviest, second heaviest and the SM-like neutral Higgs bosons, respectively. The mere presence of this decay channel, which is non-zero only away from the alignment limit, 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.