Generalised CP and Δ(6n²) Family Symmetry in Semi-Direct Models of Leptons

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We perform a detailed analysis of Δ(6n²) family symmetry combined with a generalised CP symmetry in the lepton sector, breaking to different remnant symmetries Gν in the neutrino and Gₗ in the charged lepton sector, together with different remnant CP symmetries in each sector. We discuss the resulting mass and mixing predictions for Gν=Z₂ with Gₗ=K₄,Zₚ,p>2 and Gν=K₄ with Gₗ=Z₂. 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.