solution [@NSW1] is provided by the addition of a singlet $S.$ Soft terms that break supersymmetry can induce a v.e.v. for $S$ and an effective supersymmetric mass $\mu =\lambda S$ of the right order magnitude. This mechanism asks for the $\kappa S^{3}/3$ self-coupling in the superpotential which also breaks the unwanted Peccei-Quinn symmetry. However, this coupling would be forbidden and the singlet model inoperative if $S$ has non-trivial quantum numbers with respect to broken symmetries beyond those of the Standard Model. This phenomenon is frequently found in superstring compactifications. We take here the pragmatic viewpoint that all the dimension three interactions that preserve the low-energy local and global symmetries are to be included. As we shall discuss later, very low values of the coupling $\kappa $ are consistent with the phenomenological constraints. In this case, it could be a relic of non-renormalizable interactions after the decoupling of, $e.g.,$ extra $U(1)$ gauge symmetries. Actually, the “sliding” singlet v.e.v. compensates for the smallness of the couplings $\kappa $ and $\lambda $ and this considerably reduces the fine-tuning problem of the $\mu $-term. Such a possibility is indeed supported by our analysis.

Supersymmetric mass terms are forbidden by the $\ZZ_{3}$ symmetry of the 