to $1$ in the SUSY basis. implies that the invariant and pseudo-invariant Higgs fields defined in are related in the supersymmetric limit, H\_U=H\_U\^&=&e\^[i]{}\_D=e\^[i]{}\_D\^,\[mssmhu\]\
H\_D=H\_D\^&=&e\^[-i]{}\_U=e\^[-i]{}\_U\^,\[mssmhd\] for the hypercharge $+1$ and hypercharge $-1$ MSSM Higgs fields, respectively. If we now insert into , we find that the coefficients of the Higgs potential in the SUSY basis are $\mathcal{Y}_{DD},\mathcal{Y}_{UU},e^{i\eta}\mathcal{Y}_{UD},
\mathcal{Z}_{UU,UU},\mathcal{Z}_{DD,DD},\mathcal{Z}_{DD,UU},\mathcal{Z}_{DU,UD},e^{2i\eta}\mathcal{Z}_{DU,DU},
e^{i\eta}\mathcal{Z}_{DD,DU},e^{i\eta}\mathcal{Z}_{UU,UD}$, subject to the conditions of . Note that when the conditions of are imposed, the phase $\eta$ drops out completely. Indeed, the nonzero Higgs potential parameters in the SUSY basis, $\mathcal{Y}_{DD},\mathcal{Y}_{UU},\mathcal{Z}_{UU,UU},\mathcal{Z}_{DD,DD},\mathcal{Z}_{DD,UU},\mathcal{Z}_{DU,UD}$ are physical observables that are real and invariant with respect to U(2)-basis transformations The existence of a physical SUSY basis is not surprising. Consider the higgsino Majorana mass term, which arises from a supersymmetric term in the MSSM superpotential, $$\mu \epsilon_{ij} \psi^i_{H_D} \psi^j_{H_U}.
\label{fix}$$ A THDM basis transformation mixes $\Phi_1$ and $\Phi_2$, which corresponds to a transformation between the MSSM Higgs fields, $H_U$ with $H_D^\dagger$. But the Higgs fields belong to Higgs superfields whose scalar and fermionic components are $(H_U, \psi_{H_U})$ and $(H_D, \psi_{H_D})$. As a result, one cannot apply a general U(2)-basis transformation to the full Higgs supermultiplets consistent with supersymmetry. Thus, Eq. (\[fix\]) effectively defines a preferred basis for 