Higgs fields. We shall write these couplings in a form that is manifestly independent of the choice of basis for the Higgs fields: \[gensusygaugino\] [L]{}\_= \^\^\_[ij]{}(\^j\_[H\_U]{}f\_U\^a\_a\^[i]{} +\^[ik]{}\^j\_[H\_D]{}f\_D\^[a]{}\_a\^k) +\^(\^i\_[H\_U]{} f\^[a]{}\_U\_a\^[i]{} -\^[ik]{}\^i\_[H\_D]{}f\^[a]{}\_D\_a\^k)+[h.c.]{}, where the couplings $f^a_U$, $f^a_D$, $f^{\prime\,a}_U$, and $f^{\prime\,a}_D$ transform covariantly under a Higgs basis U(2)-transformation,[^7] f\^a\_[U,D]{}U\_[ab]{}f\^b\_[U,D]{},f\^[a]{}\_[U,D]{}U\_[ab]{}f\^[b]{}\_[U,D]{}. In the supersymmetric limit, there is a natural choice of basis for the Higgs fields, henceforth called the *SUSY basis*, in which: \[spbasis\] f\_U\^a=g\^[a2]{},f\_D\^[a]{}=g\^[a1]{},f\_U\^[a]{}=g’\^[a2]{},f\_D\^[a]{}=g’\^[a1]{}. In particular, in the SUSY basis, the so-called “wrong-Higgs interactions” of Ref. [@HM] are absent in the supersymmetric limit. However, under a general Higgs basis transformation, the supersymmetric gaugino-higgsino-Higgs Lagrangian will transform into a linear combination of supersymmetric and wrong-Higgs interaction terms. Thus, in a generic basis choice for the Higgs fields, the supersymmetry is not manifest. One of the goals of this section is to determine a set of basis-independent conditions that guarantees the existence of a basis choice in which is satisfied. Such basis-independent conditions would constitute an invariant signal for manifestly supersymmetric Higgs interactions.

The couplings $f^a_U$, $f_D^a$, $f^{\prime\,a}_U$, and $f^{\prime\,a}_D$ are complex vectors that live in the two-dimensional Higgs flavor space. It is convenient to define the corresponding unit vectors, $\hat f^a\equiv f^a/|f|$, where $|f|\equiv (f^{a\,\ast} 