Invariant approach to CP in family symmetry models

Abstract

We propose the use of basis invariants, valid for any choice of CP transformation, as a powerful approach to studying specific models of CP violation in the presence of discrete family symmetries. We illustrate the virtues of this approach for examples based on $A_4$ and $\Delta (27)$ family symmetries. For $A_4$, we show how to elegantly obtain several known results in the literature. In $\Delta (27)$ we use the invariant approach to identify how explicit (rather than spontaneous) CP violation arises, which is geometrical in nature, i.e. persisting for arbitrary couplings in the Lagrangian.

4 pages plus references. v2: to be published in PRD

References in corpus (9)

• Observation of electron-antineutrino disappearance at Daya Bay
• Neutrino tri-bi-maximal mixing from a non-Abelian discrete family symmetry
• S_4 Flavored CP Symmetry for Neutrinos
• 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
• Supersymmetric Jarlskog Invariants: the Neutrino Sector
• Symmetries of symmetries and geometrical CP violation
• Geometrical CP violation in the N-Higgs-doublet model

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• Leptogenesis and residual CP symmetry
• $A_4$ and CP symmetry and a model with maximal CP violation
• CP Symmetry and Lepton Mixing from a Scan of Finite Discrete Groups
• Classifying CP transformations according to their texture zeros: theory and implications
• Alternative Schemes of Predicting Lepton Mixing Parameters from Discrete Flavor and CP Symmetry
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• Quark and Lepton Mixing Patterns from a Common Discrete Flavor Symmetry with Generalized CP
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• The symmetry approach to quark and lepton masses and mixing
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• CP-odd invariants for multi-Higgs models: applications with discrete symmetry
• Implications of residual CP symmetry for leptogenesis in a model with two right-handed neutrinos
• Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries
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• A New Littlest Seesaw Model
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• Spontaneous CP violation in multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• Low scale type I seesaw model for lepton masses and mixings
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• CP and other Symmetries of Symmetries
• Adding CP to flavour symmetries
• Dihedral flavor group as the key to understand quark and lepton flavor mixing