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- Symmetries of the 2HDM: an invariant formulation and consequencesPublication . Ferreira, Pedro Miguel; Grzadkowski, B.; Ogreid, Odd Magne; Osland, P.Symmetries of the Two-Higgs-Doublet Model (2HDM) potential that can be extended to the whole Lagrangian, i.e. the CP-symmetries CP1, CP2, CP3 and the Higgs-family symmetries Z(2), U(1) and SO(3) are discussed. Sufficient and necessary conditions in terms of constraints on masses and physical couplings for the potential to respect each of these symmetries are found. Each symmetry can be realized through several alternative cases, each case being a set of relations among physical parameters. We will show that some of those relations are invariant under the renormalization group, but others are not. The cases corresponding to each symmetry group are illustrated by analyzing the interplay between the potential and the vacuum expectation values.
- Softly broken symmetries in the 2HDM: an invariant formulationPublication . Ferreira, Pedro Miguel; Grzadkowski, Bohdan; Ogreid, Odd Magne; Osland, PerSoft breaking of a symmetry requires an invariance of the dimension-4 part of the Lagrangian and non-trivial variation of the lower-dimensional part. However, in general, separation between the dim-4 and lower-dimensional Lagrangian is not invariant with respect to basis transformations of fields. Therefore, a natural question of the physical meaning of soft symmetry breaking arises. This problem is addressed here in the framework of two-Higgs-Doublet Models (2HDM). It has been shown, within these models, that in spite of the ambiguity corresponding to the separation between dim-4 and the lower-dimension Lagrangian, implications of the soft symmetry breaking could be formulated in terms of observables, i.e., they are physical and measurable. There are six global symmetries that can be imposed on the scalar sector of the generic 2HDM. Necessary and sufficient tree-level conditions for soft breaking of all of them have been formulated in terms of observables.