also distinguish between the two cases where the minimum ($%
0,0,x\neq 0$) of the potential does exist or not. The second case could be ensured by choosing the parameter $A_{\lambda }$ in (\[X0\]) to be extremely negative, then $x$ does not exist. This is easier to satisfy in region **(1)**. In both cases, the condition (\[zpm\]) is, almost, automatically fulfilled within (\[zmix\]).

Also, one needs to know the effect of the phase $\theta$ on the EWPT strength. At tree-level (\[Vv\]), this phase is not relevant due to the choice of $A_{\lambda}$, but the thermal corrections depend on this phase through all the fields masses expect gauge bosons and top quark. Therefore, we consider the values $0<\theta_{0}<\pi/3$.

The mass parameters: $m_{Q}$, $m_{U}$, $A_{t}$, $M_{2}$, $M_{1}$, and $%
M_{1}^{\prime }$ appear at one-loop level in the effective potential, therefore we expect that their role is less important in the EWPT dynamics. Indeed, these parameters will change the field masses and therefore could make ($\upsilon _{1},\upsilon _{2},\upsilon _{x}e^{i\theta _{0}}$) a local minimum instead of the global one through the corrections in (\[V1\]). However, the parameters: $g^{\prime }$, $\lambda $, $\upsilon _{x}$ and $%
\tan \beta $, as well the charges $Q^{\prime }$s that 