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See detailClassification of finite reparametrization symmetry groups in the three-Higgs-doublet model
Ivanov, Igor ULg; Vdovin, Evgeny

in European Physical Journal C -- Particles & Fields (2013), 73

Symmetries play a crucial role in electroweak symmetry breaking models with non-minimal Higgs content. Within each class of these models, it is desirable to know which symmetry groups can be implemented ... [more ▼]

Symmetries play a crucial role in electroweak symmetry breaking models with non-minimal Higgs content. Within each class of these models, it is desirable to know which symmetry groups can be implemented via the scalar sector. In N-Higgs-doublet models, this classification problem was solved only for N=2 doublets. Very recently, we suggested a method to classify all realizable finite symmetry groups of Higgs-family transformations in the three-Higgs-doublet model (3HDM). Here, we present this classification in all detail together with an introduction to the theory of solvable groups, which play the key role in our derivation. We also consider generalized-CP symmetries, and discuss the interplay between Higgs-family symmetries and CP-conservation. In particular, we prove that presence of the $Z_4$ symmetry guarantees the explicit CP-conservation of the potential. This work completes classification of finite reparametrization symmetry groups in 3HDM. [less ▲]

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See detailSymmetries in multi-Higgs-doublet models
Ivanov, Igor ULg; Vdovin, Evgeny

in AIP Conference Proceedings (2013)

We report the recent progress in understanding of symmetries which can be implemented in the scalar sector of electroweak symmetry breaking models with several Higgs doublets. In particular we present the ... [more ▼]

We report the recent progress in understanding of symmetries which can be implemented in the scalar sector of electroweak symmetry breaking models with several Higgs doublets. In particular we present the list of finite reparametrization symmetry groups which can appear in the three-Higgs-doublet models. [less ▲]

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See detailDiscrete symmetries in the three-Higgs-doublet model
Ivanov, Igor ULg; Vdovin, Evgeny

in Physical Review. D : Particles and Fields (2012), 86(9), 0950305

N-Higgs-doublet models (NHDM) are among the most popular examples of electroweak symmetry breaking mechanisms beyond the Standard Model. Discrete symmetries imposed on the NHDM scalar potential play a ... [more ▼]

N-Higgs-doublet models (NHDM) are among the most popular examples of electroweak symmetry breaking mechanisms beyond the Standard Model. Discrete symmetries imposed on the NHDM scalar potential play a pivotal role in shaping the phenomenology of the model, and various symmetry groups have been studied so far. However, in spite of all efforts, the classification of finite Higgs-family symmetry groups realizable in NHDM for any N>2 is still missing. Here, we solve this problem for the three-Higgs-doublet model by making use of Burnside’s theorem and other results from pure finite group theory which are rarely exploited in physics. Our method and results can also be used beyond high-energy physics, for example, in the study of possible symmetries in three-band superconductors. [less ▲]

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See detailAbelian symmetryies in NHDM
Keus, Venus ULg; Ivanov, Igor ULg; Vdovin, Evgeny

Diverse speeche and writing (2012)

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See detailAbelian symmetries in multi-Higgs-doublet models
Ivanov, Igor ULg; Keus, Venus ULg; Vdovin, Evgeny

in Journal of Mathematical Physics (2012)

N-Higgs-doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a ... [more ▼]

N-Higgs-doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a certain symmetry group. Although several such groups have been used, no general analysis of symmetries possible in the NHDM scalar sector exists. Here, we describe a strategy that identifies all abelian groups which are realizable as symmetry groups of the NHDM Higgs potential. We consider both the groups of Higgs-family transformations only and the groups which also contain generalized CP transformations. We illustrate this strategy with the examples of 3HDM and 4HDM and prove several statements for arbitrary N. [less ▲]

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