Basis-independent methods for the two-Higgs-doublet model. II. The Significance of tan$\beta$

By S. Davidson, H. Haber. 2005

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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, ${\ensuremath{\Phi}}_{a}$ $(a=1,2)$. 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, $\mathrm{tan}\ensuremath{\beta}\ensuremath{\equiv}⟨{\ensuremath{\Phi}}_{2}^{0}⟩/⟨{\ensuremath{\Phi}}_{1}^{0}⟩$ 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 $\mathrm{tan}\ensuremath{\beta}$. In specialized versions of the 2HDM, $\mathrm{tan}\ensuremath{\beta}$ 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 ``$\mathrm{tan}\ensuremath{\beta}$-like'' parameters that are manifestly basis-independent. The minimal supersymmetric extension of the standard model provides a simple framework for exhibiting such effects.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b9765b516ed3a2a2c833d1118a550ae4e44c86ae