purely cubic superpotential assumed in (\[A\]). This discrete symmetry also prevents $S$ from getting a large v.e.v. through large radiative corrections to singlet tadpole terms, which invalidate other supersymmetric models with gauge singlets [@Posus; @Elba]. On the other hand, the $\ZZ_3$ symmetry can give rise to cosmological problems in the form of domain walls which are produced during the electroweak phase transition [@Abel]. Possible solutions to this problem have been discussed in [@Abel] and include inflation of the weak scale, embedding of the discrete symmetry into a gauge symmetry at the Planck scale or re-introducing of the $\mu$-term in the superpotential. (In the presence of the singlet, $\mu$ can be orders of magnitudes smaller than the weak scale, in which case our subsequent analysis is not affected; however, the $\mu$-problem was part of the motivations of the model.) In any case, since we concentrate in this paper on the particle physics aspects of the model and do not discuss cosmological issues, our results will be independent of the form of the solutions of the domain wall problem.

The study of spontaneous CP breaking in the (M+1)SSM also differs from the MSSM. Indeed, CP violating vacua can be induced only if 