Spontaneous CP violation in supersymmetric models

We briefly comment on the question of spontaneous CP violation for several models of weak interactions. We focus on one of the minimal extensions of the Standard Model where spontaneous CP violation is viable,the next-to-minimal supersymmetric standard model (NMSSM), with two Higgs doublets and a gauge singlet. We analyse the most general Higgs potential without a discrete Z_3 symmetry, and derive an upper bound on the mass of the lightest neutral Higgs boson. We estimate $\epsilon_K$ by applying the mass insertion approximation, finding that in order to account for the observed CP violation in the neutral kaon sector a non-trivial flavour structure in the soft-breaking A-terms is required and that the upper bound on the lightest Higgs-boson mass becomes stronger. We also discuss the implications of electric dipole moments of the electron and the neutron in SUSY models with SCPV.