Softly broken symmetries in the 2HDM — an invariant formulation

Soft breaking of a symmetry requires an invariance the dimension-4 part Lagrangian and non-trivial variation lower-dimensional part. However, in general, separation between dim-4 is not invariant with respect to basis transformations fields. Therefore, natural question physical meaning soft arises. This problem addressed here framework two-Higgs-Doublet Models (2HDM). It has been shown, within these models, that spite ambiguity corresponding lower-dimension Lagrangian, implications could be formulated terms observables, i.e., they are measurable. There six global symmetries can imposed on scalar sector generic 2HDM. Necessary sufficient tree-level conditions for all them have observables.