Basis-independent methods for the two-Higgs-doublet model. II. The significance oftanβ

Abstract

In the most general two-Higgs-doublet model (2HDM), there is no distinction between the two complex hypercharge-one $\mathrm{SU}(2{)}_{\mathrm{L}}$ doublet scalar fields, ${\Phi }_a$ $(a=1,2)$. Thus, any two orthonormal linear combinations of these two fields can serve as a basis for the Lagrangian. All physical observables of the model must be basis-independent. For example, $\tan \beta \equiv ⟨{\Phi }_2^0⟩/⟨{\Phi }_1^0⟩$ is basis-dependent and thus cannot be a physical parameter of the model. In this paper, we provide a basis-independent treatment of the Higgs sector with particular attention to the neutral Higgs boson mass-eigenstates, which generically are not eigenstates of $CP$. We then demonstrate that all physical Higgs couplings are indeed independent of $\tan \beta$. In specialized versions of the 2HDM, $\tan \beta$ can be promoted to a physical parameter of the Higgs-fermion interactions. In the most general 2HDM, the Higgs-fermion couplings can be expressed in terms of a number of physical “$\tan \beta$-like” parameters that are manifestly basis-independent. The minimal supersymmetric extension of the standard model provides a simple framework for exhibiting such effects.