of the Higgs boson. Much attention has been devoted to the minimal supersymmetric extension of the standard model (MSSM), which requires two complex Higgs doublets and superpartners for all Standard Model particles [@MSSM].

In general, there is no fundamental reason why the SM should possess only one complex Higgs doublet. The most well-studied extended Higgs sector is that of the two-Higgs-doublet model (THDM) [@THDM]. The scalar potential of the most general THDM involves 14 parameters. Of these parameters, only eleven combinations are physical, as three degrees of freedom can be absorbed into a redefinition of the Higgs fields [@Lav; @DavHab]. This number may be further reduced by imposing some symmetry requirements on the Higgs Lagrangian. But, identifying such symmetries is complicated by the fact that one may perform a basis transformation of the Higgs fields. A symmetry that looks simple in one basis may be completely obscured in another basis. Hence, it is important to develop basis-invariant signals of such symmetries, which can identify the physically meaningful and experimentally accessible parameters in the theory. The need to seek basis invariant observables in models with many Higgs bosons was pointed out by Lavoura and Silva [@LS], and by Botella and Silva 