On radiative CP violation in (supersymmetric) two Higgs doublet models

We discuss the feasibility of spontaneous CP violation being induced by radiative corrections in 2HDMʹs, emphasizing on a consistent treatment at 1-loop level. Specifically, we analyze the cases of gaugino/higgsino effect on MSSM, and a new model proposed here with an extra, exotic, quark doublet. The latter model is phenomenologically interesting. One conclusion is that some fine tuning is in general needed for the scenario to work. The case for the new model requires a tree level mass mixing between the two Higgses, which fits in the standard SUSY picture. The fine tuning requires is then very moderate in magnitude and in a way natural.