Symmetry breaking patterns in 3HDM

Abstract

An attractive feature of New Physics models with multiple Higgs fields is that they are equipped with discrete symmetry groups in the Higgs and flavour sectors. These symmetry groups are often broken at the global minimum of the Higgs potential, either completely or to a proper subgroup, with certain phenomenological consequences. Here, we systematically explore these symmetry breaking patterns in the scalar sector of the three-Higgs-doublet model (3HDM). We use the full list of discrete symmetry groups allowed in 3HDM, and for each group we find all possible ways it can break by the Higgs vacuum expectation value alignment. We also discuss the interplay between these symmetry groups and various forms of CP-violation in the scalar sector of 3HDM. Not only do our results solve the problem for 3HDM, but they also hint at several general features in multi-scalar sectors.

24 pages, 5 figures, 2 tables; v2: expanded introduction, matches published version

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• Recognizing symmetries in 3HDM in basis-independent way
• Symmetries of symmetries and geometrical CP violation
• Flavour and CP predictions from orbifold compactification
• Spontaneous CP violation in multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• CP and other Symmetries of Symmetries
• Compatible abelian symmetries in N-Higgs-Doublet Models
• One-loop considerations for coexisting vacua in the CP conserving 2HDM
• A Three Doublet Lepton-Specific Model