Basis-independent methods for the two-Higgs-doublet model

In the most general two-Higgs-doublet model (2HDM), unitary transformations between the two Higgs fields do not change the functional form of the Lagrangian. All physical observables of the model must therefore be independent of such transformations (i.e., independent of the Lagrangian basis choice for the Higgs fields). We exhibit a set of basis-independent quantities that determine all tree-level Higgs couplings and masses. Some examples of the basis-independent treatment of 2HDM discrete symmetries are presented. We also note that the ratio of the neutral Higgs field vacuum expectation values, $\tan \beta$, is not a meaningful parameter in general, as it is basis dependent. Implications for the more specialized 2HDMs (e.g., the Higgs sector of the minimal supersymmetric extension of the standard model and the so-called type-I and type-II 2HDMs) are explored.

Figure 1

Diagrammatic representation of covariant tensors. The two point vertices $V_{a\overline{b}}$ and $Y_{a\overline{b}}$ are indicated by the symbols $\otimes$ and $\times$, respectively. The four-point vertex $Z_{a\overline{b}c\overline{d}}$ is depicted by four line segments (meeting at the vertex point) where the indices appear in clockwise order. Unbarred (barred) indices are represented by incoming (outgoing) directed line segments.

Figure 2

The one-loop bubble diagrams corresponding to (a) $Z_{a\overline{c}}^{(1)}=Z_{a\overline{b}b\overline{c}}$ and (b) $Z_{b\overline{c}}^{(2)}=Z_{a\overline{a}b\overline{c}}$. These two diagrams are distinguished, since the $Z$-vertex must be read in a clockwise fashion.

Figure 3

Diagrams corresponding to the potentially complex invariants of Eq. (51).