Higgs alignment and novel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> -violating observables in two-Higgs-doublet models

Null results from searches for new physics at the Large Hadron Collider (LHC) tend to enforce belief that particles must be much heavier than weak scale. We undertake a systematic study of interplay between Higgs alignment and $CP$-violation in complex two-Higgs-doublet models, which enables us construct $CP$-violating scenario where bosons are close scale after including stringent constraints electric dipole moment measurements LHC. In addition, we propose novel potential signal Higgs-to-Higgs decays, ${h}_{3}\ensuremath{\rightarrow}{h}_{2}{h}_{1}$, ${h}_{3}$, ${h}_{2}$, ${h}_{1}$ heaviest, second heaviest Standard Model-like neutral bosons, respectively. The decay could manifest itself triple boson final states ${h}_{1}{h}_{1}{h}_{1}$ ${h}_{1}{h}_{1}Z$, quite distinct provide unique venues