$\Phi_1$ and $\Phi_2$ within the MSSM. This is why the SUSY basis has a physical significance.

\[sec:tanb\]Invariant $\boldsymbol{\tan\beta}$-like parameters
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Until this subsection, we have made no assumptions about the nature of the Higgs vacuum. In the supersymmetric limit of the MSSM, the minimum of the tree-level potential resides at zero field and there is no electroweak symmetry breaking. After dimension-two soft-supersymmetry-breaking terms are included, it becomes possible to break the SU(2)$\times$U(1) symmetry of the scalar potential down to U(1)$_{\rm EM}$. In the generic basis, we define vacuum expectation values, \^0\_a= v\_avv\_a, where $\hat v_a$ is a complex unit vector in the two-dimensional Higgs flavor space and $v\simeq 246~{\rm GeV}$. In the MSSM, the parameter $\tan\beta$ is defined in the SUSY basis,[^11] . However, in the most general THDM, $\tan\beta$ is a basis-dependent concept that does not correspond to any physical observable. In Ref. [@oneil], a number of invariant parameters connected to the Higgs-fermion Yukawa couplings are introduced that play the role of $\tan\beta$ in constrained THDMs. Here, we shall indicate how to define $\tan\beta$-like parameters associated with the gaugino-higgsino-Higgs interactions.

The basic idea is to define $\tan\beta$ as the ratio of vacuum expectation values in the quasi-physical bases introduced 