Horizontal Symmetries $\Delta (150)$ and $\Delta (600)$

Abstract

Using group theory of mixing to examine all finite subgroups of SU(3) with an order less than 512, we found recently that only the group $\Delta (150)$ can give rise to a correct reactor angle ${þ}_{13}$ of neutrino mixing without any free parameter. It predicts ${\sin }^{2}2{þ}_{13}=0.11$ and a sub-maximal atmospheric angle with ${\sin }^{2}2{þ}_{23}=0.94$, in good agreement with experiment. The solar angle ${þ}_{12}$, the CP phase $\d$, and the neutrino masses $m_i$ are left as free parameters. In this article we provide more details of this case, discuss possible gain and loss by introducing right-handed symmetries, and/or valons to construct dynamical models. A simple model is discussed where the solar angle agrees with experiment, and all its mixing parameters can be obtained from the group $\Delta (600)$ by symmetry alone. The promotion of $\Delta (150)$ to $\Delta (600)$ is on the one hand analogous to the promotion of $S_3$ to $S_4$ in the presence of tribimaximal mixing, and on the other hand similar to the extension from $A_4$ to $S_4$ in that case.

version to appear in Phys. Rev. D

References in corpus (9)

• The Unique Horizontal Symmetry of Leptons
• The Horizontal Symmetry for Neutrino Mixing
• Symmetry of Lepton Mixing
• The Flavor Group Delta(6n^2)
• Mass Independent Textures and Symmetry
• Magic Neutrino Mass Matrix and the Bjorken-Harrison-Scott Parameterization
• Group Theory and Dynamics of Neutrino Mixing
• Neutrino Mixing and Discrete Symmetries
• Horizontal Symmetry

Cited by in corpus (13)

• Trimaximal TM1 neutrino mixing in S4 with spontaneous CP violation
• Lepton Mixing from Delta (3 n^2) and Delta (6 n^2) and CP
• Mixing angle and phase correlations from A5 with generalised CP and their prospects for discovery
• Lepton Mixing Predictions including Majorana Phases from $\Delta (6n^2)$ Flavour Symmetry and Generalised CP
• Quark and Leptonic Mixing Patterns from the Breakdown of a Common Discrete Flavor Symmetry
• Predictions for Leptonic Mixing Angle Correlations and Non-trivial Dirac CP Violation from $A_5$ with Generalised CP Symmetry
• Dirac Neutrinos with $S_4$ Flavor Symmetry in Warped Extra Dimensions
• Lepton and Quark Mixing Patterns from Finite Flavor Symmetries
• [Re]constructing Finite Flavour Groups: Horizontal Symmetry Scans from the Bottom-Up
• Residual Z2 x Z2 symmetries and lepton mixing
• A Built-in Horizontal Symmetry of $SO(10)$
• Lepton Mixing, Residual Symmetries, and Trigonometric Diophantine Equations
• Neutrino Mixing from $\Delta (6n^2)$ Groups