Generalised CP and $\Delta (6n^2)$ Family Symmetry in Semi-Direct Models of Leptons

Abstract

We perform a detailed analysis of $\Delta (6n^2)$ family symmetry combined with a generalised CP symmetry in the lepton sector, breaking to different remnant symmetries $G_{\nu }$ in the neutrino and $G_l$ in the charged lepton sector, together with different remnant CP symmetries in each sector. We discuss the resulting mass and mixing predictions for $G_{\nu }=Z_2$ with $G_l=K_4,Z_p,p>2$ and $G_{\nu }=K_4$ with $G_l=Z_2$. All cases correspond to the preserved symmetry smaller than the full Klein symmetry, as in the semi-direct approach, leading to predictions which depend on a single undetermined real parameter, which mainly determines the reactor angle. We focus on five phenomenologically allowed cases for which we present the resulting predictions for the PMNS parameters as a function of $n$, as well as the predictions for neutrinoless double beta decay.

65 pages, 19 figures, and the predictions for neutrinoless double beta decay are updated

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• Alternative Schemes of Predicting Lepton Mixing Parameters from Discrete Flavor and CP Symmetry
• The symmetry approach to quark and lepton masses and mixing
• Lepton Mixing in $A_5$ Family Symmetry and Generalized CP
• A Survey of Neutrino Flavor Models and the Neutrinoless Double Beta Decay Funnel
• Perspectives for tests of neutrino mass generation at the GeV scale: Experimental reach versus theoretical predictions
• Tribimaximal Mixing in the $SU(5)\times {\mathcal{T}}_{13}$ Texture
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• Residual $Z_2$ symmetries and leptonic mixing patterns from finite discrete subgroups of $U(3)$
• Low-scale leptogenesis with flavour and CP symmetries
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• Dihedral flavor group as the key to understand quark and lepton flavor mixing
• Flavour anomalies meet flavour symmetry
• CP-like Symmetry with Discrete and Continuous Groups and CP Violation/Restoration
• Neutrino Oscillations in the Three Flavor Paradigm