Symmetries of the 2HDM: an invariant formulation and consequences

Abstract

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 Z2, 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.

58 pages, 7 figures. JHEP version. References added, clarifications and minor changes made

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• Vacuum Stability in the one-loop approximation of a 331 Model
• Systematic analysis of 3HDM symmetries
• The general Two-Higgs Doublet Model in a gauge-invariant form
• Tridiagonal scalar mass matrix in the CP4 3HDM and its implications
• Lattice investigation of custodial two-Higgs-doublet model at weak quartic couplings
• Roads for Right-handed Neutrino Dark Matter: Fast Expansion, Standard Freeze-out, and Early Matter Domination
• CP violation in H^\pm \to W^\pm Z: A physical approach for the 2HDM
• Accidental symmetries in the scalar potential of the Standard Model extended with two Higgs triplets