Journal of High Energy Physics

, 2017:136 | Cite as

Spontaneous CP violation in multi-Higgs potentials with triplets of Δ(3n2) and Δ(6n2)

  • Ivo de Medeiros Varzielas
  • Stephen F. King
  • Christoph Luhn
  • Thomas NederEmail author
Open Access
Regular Article - Theoretical Physics


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 Δ(3n2) and Δ(6n2) series, including A4, S4, Δ(27) and Δ(54). For each case, we give the potential and find various global minima 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 geometrical phases.


CP violation Discrete Symmetries Higgs Physics Beyond Standard Model 


Open Access

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Ivo de Medeiros Varzielas
    • 1
    • 2
  • Stephen F. King
    • 1
  • Christoph Luhn
    • 3
  • Thomas Neder
    • 1
    • 4
    Email author
  1. 1.School of Physics and AstronomyUniversity of SouthamptonSouthamptonUnited Kingdom
  2. 2.CFTP, Departamento de Física, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal
  3. 3.Theoretische Physik 1, Naturwissenschaftlich-Technische FakultätUniversität SiegenSiegenGermany
  4. 4.AHEP Group, Institut de Física Corpuscular — C.S.I.C./Universitat de ValènciaPaterna (Valencia)Spain

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