Discrete flavour symmetries for degenerate solar neutrino pair and their predictions

Abstract

Flavour symmetries appropriate for describing a neutrino spectrum with degenerate solar pair and a third massive or massless neutrino are discussed. We demand that the required residual symmetries of the leptonic mass matrices be subgroups of some discrete symmetry group $G_f$. $G_f$ can be a subgroup of SU(3) if the third neutrino is massive and we derive general results on the mixing angle predictions for various discrete subgroups of SU(3). The main results are: (a) All the SU(3) subgroups of type C fail in simultaneously giving correct ${\theta }_{13}$ and ${\theta }_{23}$. (b) All the groups of type D can predict a relation ${\cos }^2{\theta }_{13}{\sin }^2{\theta }_{23}=\frac{1}{3}$ among the mixing angles which appears to be a good zeroth order approximation. Among these, various $\Delta (6n^2)$ groups with $n\ge 8$ can simultaneously lead also to ${\sin }^2{\theta }_{13}$ in agreement with global fit at 3$\sigma$. (c) The group $\Sigma (168)\cong PSL(2,7)$ predicts near to the best fit value for ${\theta }_{13}$ and ${\theta }_{23}$ within the 1$\sigma$ range. All discrete subgroups of U(3) with order $<512$ and having three dimensional irreducible representation are considered as possible $G_f$ when the third neutrino is massless. Only seven of them are shown to be viable and three of these can correctly predict ${\theta }_{13}$ and/or ${\theta }_{23}$. The solar angle remains undetermined at the leading order in all the cases due to degeneracy in the masses. A class of general perturbations which can correctly reproduce all the observables are discussed in the context of several groups which offer good leading order predictions.

arXiv comment25 pages, 7 figures

References in corpus (39)

• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Non-Abelian Discrete Symmetries in Particle Physics
• Neutrino Mass and Mixing with Discrete Symmetry
• Softly Broken A_4 Symmetry for Nearly Degenerate Neutrino Masses
• Results on neutrinoless double beta decay of 76Ge from GERDA Phase I
• Theory of Neutrinos: A White Paper
• Status of three-neutrino oscillation parameters, circa 2013
• Finite Modular Groups and Lepton Mixing
• Lepton mixing and discrete symmetries
• The Unique Horizontal Symmetry of Leptons
• The Horizontal Symmetry for Neutrino Mixing
• Symmetry of Lepton Mixing
• Discrete Flavour Symmetries in Light of T2K
• The Flavor Group Delta(3n^2)
• The Flavor Group Delta(6n^2)
• Lepton Mixing Predictions from Delta(6n^2) Family Symmetry
• Lepton Mixing Patterns from a Scan of Finite Discrete Groups
• Finite flavour groups of fermions
• Discrete symmetries and model-independent patterns of lepton mixing
• Tri-Bimaximal Neutrino Mixing and Discrete Flavour Symmetries
• Simple Finite Non-Abelian Flavor Groups
• Tribimaximal Mixing From Small Groups
• Quark and Leptonic Mixing Patterns from the Breakdown of a Common Discrete Flavor Symmetry
• Finite Symmetry of Leptonic Mass Matrices
• Constraints on neutrino masses from Planck and Galaxy Clustering data
• Principal series of finite subgroups of SU(3)
• Explicit and spontaneous breaking of SU(3) into its finite subgroups
• Mixing Patterns from the Groups Sigma (n phi)
• Group Theory and Dynamics of Neutrino Mixing
• An approach to permutation symmetry for the electroweak theory
• On the finite subgroups of U(3) of order smaller than 512
• How good is μ-τsymmetry after results on non-zero θ_{13}?
• Residual Z2 x Z2 symmetries and lepton mixing
• Discrete symmetries and models of flavor mixing
• On discrete Minimal Flavour Violation
• Relating neutrino masses and mixings by discrete symmetries
• Horizontal symmetries of leptons with a massless neutrino
• A massless neutrino and lepton mixing patterns from finite discrete subgroups of U(3)
• Type I seesaw mechanism for quasi degenerate neutrinos

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