Systematic analysis of 3HDM symmetries

Abstract

Symmetries play a crucial role in shaping the structure and predictions of multi-Higgs-doublet models. In three-Higgs-doublet models considerable effort has been put into classifying possible symmetry groups and the conditions for their realisation, yet the completeness of existing classifications remains an open question. In this work, we revisit the problem of identifying realisable symmetries by re-examining conventional Higgs family and general CP transformations from an alternative perspective. Our analysis identifies certain limitations in previous approaches and introduces a clearer, more systematic framework for model builders. We expand our classification by investigating more generalised symmetry structures - the recently identified GOOFy transformations, which act non-trivially on the Higgs doublets and their conjugates. Our analysis consolidates known results, uncovers previously overlooked structures, and expands the set of symmetries in three-Higgs-doublet models, offering both a clearer theoretical foundation and a practical reference for symmetry-based model building.

V2: Clarifications and references added, V3: Further clarifications and references added

References in corpus (63)

• Non-Abelian Discrete Symmetries in Particle Physics
• Minkowski space structure of the Higgs potential in 2HDM
• The Lee-Wick Standard Model
• Stability and Symmetry Breaking in the General Two-Higgs-Doublet Model
• Minkowski space structure of the Higgs potential in 2HDM: II. Minima, symmetries, and topology
• A Twisted Custodial Symmetry in the Two-Higgs-Doublet Model
• The Flavor Group Delta(3n^2)
• Three-Higgs-doublet models: symmetries, potentials and Higgs boson masses
• Vacuum Topology of the Two Higgs Doublet Model
• Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model
• The Flavor Group Delta(6n^2)
• CP violation conditions in N-Higgs-doublet potentials
• CP Violation in the General Two-Higgs-Doublet Model: a Geometric View
• Lepton Mixing Patterns from a Scan of Finite Discrete Groups
• Generalized CP symmetries and special regions of parameter space in the two-Higgs-doublet model
• Symmetry breaking patterns in 3HDM
• Two-Higgs-doublet model from the group-theoretic perspective
• Higgs Potential in Minimal S_3 Invariant Extension of the Standard Model
• Discrete symmetries in the three-Higgs-doublet model
• Abelian symmetries in multi-Higgs-doublet models
• Abelian symmetries in multi-Higgs-doublet models
• A Higher-Derivative Lee-Wick Standard Model
• Geometric picture of generalized-CP and Higgs-family transformations in the two-Higgs-doublet model
• On the Classification of Accidental Symmetries of the Two Higgs Doublet Model Potential
• Analysis of an extended scalar sector with $S_3$ symmetry
• Radiative Corrections to Scalar Masses and Mixing in a Scale Invariant Two Higgs Doublet Model
• A CP-conserving multi-Higgs model without real basis
• Structure of potentials with $N$ Higgs doublets
• Discrete and continuous symmetries in multi-Higgs-doublet models
• Properties of the general NHDM. I. The orbit space
• Principal series of finite subgroups of SU(3)
• Classifying Accidental Symmetries in Multi-Higgs Doublet Models
• Physical parameters and basis transformations in the Two-Higgs-Doublet model
• Symmetries for SM Alignment in multi-Higgs Doublet Models
• Discriminative phenomenological features of scale invariant models for electroweak symmetry breaking
• On the finite subgroups of U(3) of order smaller than 512
• Determining the global minimum of Higgs potentials via Groebner bases - applied to the NMSSM
• CP4 miracle: shaping Yukawa sector with CP symmetry of order four
• Stability and symmetry breaking in the general three-Higgs-doublet model
• Comments on the classification of the finite subgroups of SU(3)
• Constraints on the Lee-Wick Higgs Sector
• Spontaneous symmetry breaking in the $S_3$-symmetric scalar sector
• Recognizing symmetries in 3HDM in basis-independent way
• Higgs potential in S_3 invariant model for quark/lepton mass and mixing
• Symmetries and Mass Degeneracies in the Scalar Sector
• Ultraviolet Properties of the Higgs Sector in the Lee-Wick Standard Model
• $S_3$-inspired three-Higgs-doublet models: A class with a complex vacuum
• Basis-invariant conditions for CP symmetry of order 4
• Yet another lesson on the stability conditions in multi-Higgs potentials
• Symmetries of the 2HDM: an invariant formulation and consequences
• Complex $S_3$-symmetric 3HDM
• GAP listing of the finite subgroups of U(3) of order smaller than 2000
• Phenomenology of the new light Higgs bosons in Gildener-Weinberg model
• Emergent symmetry in a two-Higgs-doublet model from quantum information and nonstabiliserness
• $U(1)$-charged Dark Matter in three-Higgs-doublet models
• The Gildener-Weinberg two-Higgs doublet model at two loops
• Softly broken symmetries in the 2HDM -- an invariant formulation
• A fully basis invariant Symmetry Map of the 2HDM
• Goofy transformations and the hierarchy problem
• RG-stable parameter relations of a scalar field theory in absence of a symmetry
• Lie symmetry analysis of the two-Higgs-doublet model field equations
• Symmetries from outer automorphisms and unorthodox group extensions
• The Lee-Wick Extension of the Two-Higgs Doublet Model

Cited by in corpus (2)

• Assessing boundedness from below in the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-symmetric three-Higgs-doublet model: algorithm and machine learning
• The Hilbert Series and the Flavor Invariants of the 3HDM