Spontaneous CP violation in multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$

Abstract

Motivated by discrete flavour symmetry models, we analyse Spontaneous CP Violation (SCPV) for potentials involving three or six Higgs fields (both electroweak doublets and singlets) which fall into irreducible triplet representations of discrete symmetries belonging to the $\Delta (3n^2)$ and $\Delta (6n^2)$ series, including $A_4$, $S_4$, $\Delta (27)$ and $\Delta (54)$. For each case, we give the potential and find various global mimima for different regions of the parameter space of the potential. Using CP-odd basis Invariants that indicate the presence of Spontaneous CP Violation we separate the VEVs into those that do or do not violate CP. In cases where CP is preserved we reveal a CP symmetry of the potential that is preserved by those VEVs, otherwise we display a non-zero CP-odd Invariant. Finally we identify interesting cases where there is Spontaneous Geometrical CP Violation in which the VEVs have calculable phases.

arXiv comment57 pages, 4 diagrams

References in corpus (48)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Theory and phenomenology of two-Higgs-doublet models
• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Non-Abelian Discrete Symmetries in Particle Physics
• Neutrino Mass and Mixing with Discrete Symmetry
• Softly Broken A_4 Symmetry for Nearly Degenerate Neutrino Masses
• Neutrino Mass and Mixing: from Theory to Experiment
• Basis-independent methods for the two-Higgs-doublet model
• Jarlskog-like invariants for theories with scalars and fermions
• Neutrino tri-bi-maximal mixing from a non-Abelian discrete family symmetry
• Minkowski space structure of the Higgs potential in 2HDM
• Fundamental CP-violating quantities in a SU(2)$\otimes$U(1) model with many Higgs doublets
• Conditions for CP-Violation in the General Two-Higgs-Doublet Model
• CP and Discrete Flavour Symmetries
• Minkowski space structure of the Higgs potential in 2HDM: II. Minima, symmetries, and topology
• Building and testing models with extended Higgs sectors
• The Flavor Group Delta(3n^2)
• Neutrino Mass Matrix from Delta(27) Symmetry
• Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model
• CP Violation in the General Two-Higgs-Doublet Model: a Geometric View
• CP-odd invariants in models with several Higgs doublets
• Symmetry breaking patterns in 3HDM
• A common origin of fermion mixing and geometrical CP violation, and its test through Higgs physics at the LHC
• Generalized CP symmetries in Delta(27) flavor models
• Geometrical CP violation from non-renormalisable scalar potentials
• Geometrical CP Violation
• Constraining Flavour Symmetries At The EW Scale I: The A4 Higgs Potential
• Two Higgs doublet models for the LHC Higgs boson data at $\sqrt{s}=$ 7 and 8 TeV
• A CP-conserving multi-Higgs model without real basis
• Properties of the general NHDM. I. The orbit space
• $A_4$ symmetry at colliders and in the universe
• Constraining Flavour Symmetries At The EW Scale II: The Fermion Processes
• Physical parameters and basis transformations in the Two-Higgs-Doublet model
• Geometrical CP violation in multi-Higgs models
• Properties of the general NHDM. II. Higgs potential and its symmetries
• Invariant approach to CP in unbroken $\Delta (27)$
• Invariant approach to CP in family symmetry models
• Spontaneous symmetry breaking in the $S_3$-symmetric scalar sector
• Symmetries of symmetries and geometrical CP violation
• CP Violating Two-Higgs-Doublet Model: Constraints and LHC Predictions
• Geometrical CP violation in the N-Higgs-doublet model
• CP-odd invariants for multi-Higgs models: applications with discrete symmetry
• Minima of multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• When the C in CP does not matter: anatomy of order-4 CP eigenstates and their Yukawa interactions
• Group-theoretic restrictions on generation of CP-violation in multi-Higgs-doublet models
• $\mathcal{C}\mathcal{P}$ violation with an unbroken $\mathcal{C}\mathcal{P}$ transformation
• Absence of Spontaneous CP violation in Multi-Higgs Doublet Extension of MSSM

Cited by in corpus (9)

• Recognizing symmetries in 3HDM in basis-independent way
• Symmetries and Mass Degeneracies in the Scalar Sector
• Flavour and CP predictions from orbifold compactification
• Three-Higgs-doublet model under A4 symmetry implies alignment
• Exploring multi-Higgs models with softly broken large discrete symmetry groups
• Effective alignments as building blocks of flavour models
• Effective alignments and the landscape of $S_4$ flavour models
• Softly-broken $A_4$ or $S_4$ 3HDMs with stable states
• Fully constrained mass matrix: Can symmetries alone determine the flavon vacuum alignments?