CP-odd invariants for multi-Higgs models: applications with discrete symmetry

Abstract

CP-odd invariants provide a basis independent way of studying the CP properties of Lagrangians. We propose powerful methods for constructing basis invariants and determining whether they are CP-odd or CP-even, then systematically construct all of the simplest CP-odd invariants up to a given order, finding many new ones. The CP-odd invariants are valid for general potentials when expressed in a standard form. We then apply our results to scalar potentials involving three (or six) Higgs fields which form irreducible triplets under a discrete symmetry, including invariants for both explicit as well as spontaneous CP violation. The considered cases include one triplet of Standard Model (SM) gauge singlet scalars, one triplet of SM Higgs doublets, two triplets of SM singlets, and two triplets of SM Higgs doublets. For each case we study the potential symmetric under one of the simplest discrete symmetries with irreducible triplet representations, namely $A_4$, $S_4$, $\Delta (27)$ or $\Delta (54)$, as well as the infinite classes of discrete symmetries $\Delta (3n^2)$ or $\Delta (6n^2)$.

54 pages, 39 diagrams, minor changes, version accepted in PRD

References in corpus (28)

• 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
• Updated fit to three neutrino mixing: status of leptonic CP violation
• Neutrino oscillations refitted
• The Flavor Group Delta(3n^2)
• The Flavor Group Delta(6n^2)
• Towards a complete $A_4\times SU(5)$ SUSY GUT
• Symmetry breaking patterns in 3HDM
• Lepton Mixing from Delta (3 n^2) and Delta (6 n^2) and CP
• Generalised CP and $\Delta (6n^2)$ Family Symmetry in Semi-Direct Models of Leptons
• Lepton Mixing Predictions including Majorana Phases from $\Delta (6n^2)$ Flavour Symmetry and Generalised CP
• Lepton Mixing Parameters from $\Delta (48)$ Family Symmetry and Generalised CP
• Discrete symmetries in the three-Higgs-doublet model
• Generalised CP and $\Delta (96)$ Family Symmetry
• A CP-conserving multi-Higgs model without real basis
• Dark Matter with Two Inert Doublets plus One Higgs Doublet
• Properties of the general NHDM. I. The orbit space
• Towards a complete $\Delta (27)\times SO(10)$ SUSY GUT
• Properties of the general NHDM. II. Higgs potential and its symmetries
• Lepton Mixing Predictions from Infinite Group Series $D_{9n,3n}^{(1)}$ with Generalized CP
• Spontaneous symmetry breaking in the $S_3$-symmetric scalar sector
• Lepton Mixing in $A_5$ Family Symmetry and Generalized CP
• Symmetries of symmetries and geometrical CP violation
• Geometrical CP violation in the N-Higgs-doublet model
• Phenomenology of the Inert (2+1) and (4+2) Higgs Doublet Models
• Models of Neutrino Mass, Mixing and CP Violation
• Compatible abelian symmetries in N-Higgs-Doublet Models
• Neutrino Mixing from $\Delta (6n^2)$ Groups

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• Revisiting Minimal Lepton Flavour Violation in the Light of Leptonic CP Violation
• Recognizing symmetries in 3HDM in basis-independent way
• Minima of multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• Spontaneous CP violation in multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• Beyond basis invariants
• Controlled fermion mixing and FCNCs in a $\Delta (27)$ 3+1 Higgs Doublet Model
• Complex $S_3$-symmetric 3HDM
• 3HDM with $\Delta (27)$ symmetry and its phenomenological consequences
• Complementary collider and astrophysical probes of multi-component Dark Matter
• Fully constrained mass matrix: Can symmetries alone determine the flavon vacuum alignments?
• $U(1)$-charged Dark Matter in three-Higgs-doublet models
• A simple criterium for CP conservation in the most general 2HDM
• Spontaneous symmetry breaking in three-Higgs-doublet $S_3$-symmetric models
• Flavour Invariants of the N Higgs Doublet Model