= - {\cal Z}_{DD,DD} - {\cal Z}_{DD,UU},
\nonumber\\*[2mm]
{\cal Z}_{DU,DU} &=& {\cal Z}_{UD,UD} = 0, \nonumber \\
{\cal Z}_{UD,DD}&=&{\cal Z}_{DU,DD}={\cal Z}_{DD,UD}={\cal Z}_{DD,DU}=0,\nonumber\\
{\cal Z}_{DU,UU}&=&{\cal Z}_{UD,UU}={\cal Z}_{UU,DU}={\cal Z}_{UU,UD}=0.
\label{calZ_ESL}\end{aligned}$$ Since these equations are basis invariant, they must hold in any theory made up of the MSSM fields with exact supersymmetry, regardless of the exact basis choice made for the Higgs fields.

That is, independently of the choice of basis for the Higgs fields, the supersymmetric limit of the Higgs/higgsino/gauge/gaugino sectors holds if and only if Eqs. (\[f\_ESL\]), (\[calY\_ESL\]) and (\[calZ\_ESL\]) hold. If Eqs. (\[f\_ESL\]) and (\[calZ\_ESL\]) hold but Eq. (\[calY\_ESL\]) does not, then supersymmetry is softly broken due to the quadratic terms of the Higgs potential. The above results fully resolves the question of the basis-invariant form for the supersymmetric limit of the THDM.

\[sec:preferred\]A preferred basis in the MSSM
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The gaugino-higgsino-Higgs interactions provide a means for defining a *quasi-physical* choice of basis. In this context, a quasi-physical basis is one in which the Higgs fields are invariant, up to a possible rephasing of one of the Higgs fields, under U(2) transformations. That is, the coefficients of the Higgs potential are either U(2)-invariants or pseudo-invariants.

There are four possible independent 