CP violation in the Standard Model with a complex singlet

CP violation of the Standard Model (SM) is insufficient to explain the baryon asymmetry in the Universe and therefore an additional source of CP violation is needed. Here we consider the extension of the SM by a neutral complex singlet and discuss the physical conditions for a spontaneous CP violation in such model. In the model there are three neutral Higgs particles. Assuming the lightest one to be the 125 GeV Higgs boson found at LHC we calculate masses of the additional Higgs scalars and perform a numerical study of the allowed region of parameters. The scenario according to which the SM-like Higgs particle comes mostly from the SM-like SU(2) doublet, with a small modification coming from the singlet, is in agreement with the newest $R_{gamma gamma}$ and precise EW (parameters S, T) data. We have found that the Jarlskog invariant, measuring the strength of the CP violation, can be enhanced as compared to the one in the SM, at the same time there is no corresponding enhancements expected for the Electric Dipole Moment (EDM).