useful region in the parameter space. Since the electroweak gauge symmetry breaking is induced by radiative corrections involving the top Yukawa coupling – a well-known property in supersymmetric extensions of the Standard Model – the existence of a physically acceptable vacuum in the (M+1)SSM is a purely quantum effect.

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[Soft terms and boundary conditions]{} {#sec: universal}
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The supersymmetric part of the scalar potential is obtained from the superpotential through the well-known expression as a sum of $F$ and $D$ terms. The supersymmetry breaking part of the lagrangian contains all soft terms consistent with the symmetries of the superpotential: gaugino masses, trilinear analytic scalar couplings and scalar mass terms. In the (M+1)SSM they are as follows (with the same notation for the chiral matter supermultiplets and their first component complex scalars) : $$\begin{aligned}
\mathcal{L}_{\mathrm{soft}}= 
&&\left( M_{1}\lambda _{1}\lambda _{1}+M_{2}\lambda _{2}\lambda
_{2}+M_{3}\lambda _{3}\lambda _{3}+\right.   \nonumber \\
&&\left. +A_{\lambda }\lambda SH_{1}\cdot H_{2}+
A_{\kappa }\frac{\kappa }{3}S^{3}+A_{t}h_{t}Q_{3}\cdot
H_{2}T^{c}+h.c\right) +\nonumber \\
&&+m_{1}^{2}\left| H_{1}\right| ^{2} +m_{2}^{2}
\left| H_{2}\right| ^{2}  
+m_{S}^{2}\left| S\right| ^{2}+m_{Q_3}^{2}\left| Q_3\right|
^{2}+m_{T}^{2}\left| T^{c}\right| ^{2}+\nonumber \\
&& +... \label{B}\end{aligned}$$ where $\lambda _{1},\lambda _{2},\lambda _{3}$ are the gauginos associated to the $U(1)_{Y},SU(2)$ and $SU(3)$ gauge symmetries. Only the terms involving the top scalars have been retained 