and $A_{\lambda }$ are usually called the SUSY soft parameters. The charges $Q^{\prime }$s should be chosen in such a way that the anomaly cancelations are ensured [@UMSSM; @UDM].

The structure of the tree-level potential (\[tree\]) seems to allow two explicit relative $CP$ violating phases between the doublets and the singlet. However, gauge invariance dictates that the only allowed phase in the potential, is that of the combination $S\epsilon _{ij}H_{1}^{i}H_{2}^{j}$, since gauge rotations can be used to set the charged Higgs vev $%
\left\langle H_{1}^{+}\right\rangle =0$, and the condition $\left\langle
H_{2}^{-}\right\rangle =0$ implies that the physical charged Higgs is nontachyonic ($M_{H^{\pm }}^{2}>0$) [@UMSSM]. Therefore, the general form of the ground state could be written as$$\left\langle H_{1}\right\rangle =\frac{\upsilon _{1}}{\sqrt{2}}\left(
\begin{array}{c}
0 \\
1%
\end{array}%
\right) ,~\left\langle H_{2}\right\rangle =\frac{\upsilon _{2}}{\sqrt{2}}%
\left(
\begin{array}{c}
1 \\
0%
\end{array}%
\right) ,~\left\langle S\right\rangle =\frac{\upsilon _{x}e^{i\theta }}{%
\sqrt{2}}.  \label{back}$$Here $\upsilon =(\upsilon _{1}^{2}+\upsilon _{2}^{2})^{1/2}=246~GeV$, and $%
\theta $ is the relative $CP$ violating phase between the singlet and the doublets; and $\theta _{0}$ its value at the ground state. The tree-level scalar potential in terms of the neutral components is given by$$\begin{aligned}
V\left( h_{1},h_{2},S\right) & =\left[ \left( g_{1}^{2}+g_{2}^{2}\right)
/4+g^{\prime 2}Q_{1}^{2}\right] h_{1}^{4}/8+\left[ \left(
g_{1}^{2}+g_{2}^{2}\right) /4+g^{\prime 2}Q_{2}^{2}\right]
h_{2}^{4}/8+g^{\prime 2}Q_{S}^{2}S^{4}/8  \notag 