The general Two-Higgs doublet eXtensions of the SM: a saucerful of secrets

We discuss the most general formulation of the Two-Higgs doublet model, which incorporates flavor changing neutral scalar interactions (FCNSI) and CP violation (CPV) from several sources. CP violation can arise either from Yukawa terms or from the Higgs potential, be it explicit or spontaneous. We show how the model, which is denoted as 2HDM-X, reduces to some versions known in the literature (2HDM-I,II,III), as well as some of their variants (top, lepton, dark) denoted here as 2HDM-IV. We also discuss another limit that includes CPV and Yukawa four textures to control FCNSI, which we denote as 2HDM-V. We evaluate the CPV asymmetry for the decay $h\to bcW$, which may allow to test the patterns of FCNSI and CPV, that arises in these models.