Abelian symmetries in multi-Higgs-doublet models

Abstract

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 make the first step towards this goal by classifying the elementary building blocks, namely the abelian symmetry groups, with a special emphasis on finite groups. 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.

33 pages, 2 figures; v2: conjecture 3 is proved and becomes theorem 3, more explanations of the main strategy are added, matches the published version

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• Recognizing symmetries in 3HDM in basis-independent way
• Classification of anomaly-free 2HDMs with a gauged U(1)' symmetry
• Geometrical CP violation in the N-Higgs-doublet model
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• Multi-Higgs-Doublet Models and Singular Alignment
• Basis-invariant conditions for CP symmetry of order 4
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• Dark CP-violation through the $Z$-portal
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• The landscape of promising non-supersymmetric string models
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• Multi-Higgs models with CP symmetries of increasingly high order
• Beyond basis invariants
• Minimal inverse-seesaw mechanism with Abelian flavour symmetries
• Multi-TeV Signals of Baryogenesis in Higgs Troika Model
• FCNC-free multi-Higgs-doublet models from broken family symmetries
• Anomaly-free axion dark matter in three Higgs doublet model and its phenomenological implications
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• Nonminimal Higgs Models, Dark Matter, and Evolution of the Universe
• Complementary collider and astrophysical probes of multi-component Dark Matter
• $U(1)$-charged Dark Matter in three-Higgs-doublet models
• Symmetries for the 4HDM: extensions of cyclic groups
• Maximally restrictive leptonic texture zeros in two-Higgs-doublet models
• A fully basis invariant Symmetry Map of the 2HDM
• Weak dipole moments of the tau lepton in models with an extended scalar sector
• Systematic analysis of 3HDM symmetries
• A Three Doublet Lepton-Specific Model
• Two-Higgs-Doublet Models with a Flavored ${\mathbb{Z}}_2$
• Lepton Flavor Specific Extended Higgs Model
• Symmetries for the 4HDM. II. Extensions by rephasing groups
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• Lie symmetry analysis of the two-Higgs-doublet model field equations
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• Computable conditions for order-2 $CP$ symmetry in NHDM potentials
• Heavy neutral pseudoscalar decays into gauge bosons in the Littlest Higgs Model
• Minimal U(1) two-Higgs-doublet models for quark and lepton flavour
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• Heavy neutral scalar decays into electroweak gauge bosons in the Littlest Higgs Model
• Assessing boundedness from below in the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-symmetric three-Higgs-doublet model: algorithm and machine learning
• Constraining the CP4-invariant three-Higgs-doublet model via top quark decays
• A three Higgs doublet model with symmetry-suppressed flavour changing neutral currents