Abstract
We provide a systematic and thorough exploration of the Δ(48) family symmetry and the consistent generalised CP symmetry. A model-independent analysis of the achievable lepton flavor mixing is performed by considering all the possible remnant symmetries in the neutrino and the charged lepton sectors. We find a new interesting mixing pattern in which both lepton mixing angles and CP phases are nontrivial functions of a single parameter θ. The value of θ can be fixed by the measured reactor mixing angle θ 13, and the excellent agreement with the present data can be achieved. A supersymmetric model based on Δ(48) family symmetry and generalised CP symmetry is constructed, and this new mixing pattern is exactly reproduced.
Highlights
-called μ − τ reflection symmetry [16,17,18,19,20,21,22], which interchanges a muon neutrino with a tau antineutrino in the charged lepton mass basis
This paper is devoted to a comprehensive analysis of lepton flavor mixing within the context of the ∆(48) family symmetry combined with generalized CP symmetry
We minimally extend the ∆(48) family symmetry to include only those nontrivial CP transformations which map one irreducible representation into its complex conjugate, the corresponding outer automorphism should be of order 2, and we find that there are three such kinds of outer automorphisms: h1 = u21, h2 = u1u2 and h3 = u31u2
Summary
We briefly review the setup which we will use to predict the mixing matrices from remnant symmetries. XνT3mν Xν3 = m∗ν , Xl†3m†l mlXl3 = (m†l ml)∗, Xν3 ∈ HCν P, Xl3 ∈ HCl P. where Xν3 and Xl3 denote the remnant CP symmetries in the neutrino and the charged lepton sectors, respectively. We will perform a model-independent study of admissible lepton mixing within ∆(48) HCP by a scan of all the possible remnant symmetries GνCP ∼= Gν HCν P and GlCP ∼= Gl HCl P, as shown in figure 1. The residual family symmetry Gl in the charged lepton sector is chosen to be an abelian cyclic subgroup Gl ∼= Zm with m ≥ 3.3 we assume that the light neutrinos are Majorana particles such that the group Gν must be restricted to the Klein subgroup K4 or a Z2 subgroup of ∆(48).
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