singlet scalar a v.e.v.. However, with the universality assumption (\[C\]), the squark and sleptons could also get non-vanishing v.e.v.’s [@Frere; @Desa; @Zwi]. Interestingly enough, the gauge interactions reduce the $A$-parameters for matter fields while preserving the value of $A_{\kappa },$ as can be seen from the expressions in the Appendix. Thus, phenomenologically consistent (M+1)SSM’s with the condition (\[C\]),(\[D\]),(\[E\]), can be build at the price of restricting the space of the supersymmetry breaking parameters. This is the most important restriction imposed on the model by the universality hypothesis, as compared to the MSSM [@ERS1]. Otherwise, the effects of this universality on the $SU(2)\times U(1)$ spontaneous breaking are similar to those in the MSSM.

Another consequence of this assumption is to reduce the number of free bare parameters in the (M+1)SSM to five (before imposing the physical constraints) just like in the MSSM: the dimensionful parameters $B$ and $\mu $ of the latter are replaced in the former by the dimensionless parameters $\lambda $ and $\kappa$.

At low energies, the soft terms as obtained from the RGE depend on the parameters $M_{0},A_{0},m_{0}^{2},$ on the choice of the GUT scale, $\Lambda
_{\mathrm{GUT}},$ through $t=$ $\ln \left(\Lambda _{\mathrm{GUT}}/v
\right)/\left(16\pi ^2\right) $ (a typical value 