(where family mixing is neglected and irrelevant for the analysis in this paper) is given by

$$\begin{aligned}
W &=&\lambda SH_{1}H_{2}+\frac{\kappa }{3}S^{3}+
h_{t}TH_{2}Q_3+h_{b}BH_{1}Q_3+h_{\tau }EH_{1}L  \nonumber \\
&&+\mathrm{(similar\ terms\ for\ the\ lighter\ quarks\ and\ leptons)} \label{A}\end{aligned}$$

where the chiral superfields are denoted as follows: $S$ (singlet), $H_{1}$ and $H_{2}$ (Higgs doublets), $T$ (antitop), $B$ (antibottom), $E$ (antitau), $Q_3$ (top-bottom doublet), $L$ (tau-neutrino doublet). Let us briefly review the present status of these motivations for the (M+1)SSM.

A supersymmetric mass term $\mu H_{1}\cdot H_{2}$ is added to the MSSM superpotential in order to avoid a potentially dangerous Peccei-Quinn symmetry and to allow for an acceptable minimum of the Higgs potential. The analysis of the $SU(2)\times U(1)$ breaking then requires $\mu $ to be roughly of the same order of magnitude as the soft terms that embody the supersymmetry breaking effects in the two Higgs sectors. This interesting hierarchy problem, the so-called $\mu $-puzzle, has motivated many a suggestion to link the supersymmetric mass $\mu $ to supersymmetry breaking [@Giuma]. In any instance, some kind of new physics is requested and in this sense the MSSM that looks mostly economical at low energies is not necessarily so at the unification $(GUT)$ level. A natural 