Higgs alignment limits in the type-II 2HDM and the MSSM with explicit CP-violation

For the general two-Higgs doublet model with Yukawa sector of type II (type II 2HDM), the Higgs alignment limit conditions are obtained for the neutral Higgs bosons with indefinite CP-parity [Formula: see text] or [Formula: see text], based on the symbolic results relating the elements of the mixing matrix to the masses of the Higgs bosons and the mixing angles. The results are valid up to dimension-six operators in the decomposition of the effective Higgs potential. Within the framework of the obtained Higgs alignment conditions the possibility of the existence of light scalars is discussed. Within the Minimal Supersymmetric Standard Model (MSSM) framework four benchmark scenarios are proposed. It is shown that two of them predict phenomenologically distinguishable CP-violating interactions of the Higgs boson [Formula: see text] with up-fermions.