Broken Democracy with Intermediate ${\mathbb{S}}_2\times {\mathbb{S}}_2$ Residual Symmetry and Random Perturbations

Abstract

The democratic mass matrix is an intriguing possibility for explaining the observed fermion mixings due to its inherent hierarchical mass eigenvalues and large mixing angles. Nevertheless, two of the three mass eigenvalues are zero if the flavor democracy is exact, in obvious contradiction with the experimental observations. One possibility is breaking the flavor democracy with anarchical perturbations as we proposed in an earlier work. However, even within the first two generations, the charged fermion masses are also hierarchical which may not be a coincidence. The democratic ${\mathbb{S}}_3^L\times {\mathbb{S}}_3^R$ symmetry of the three generations may first be broken down to an intermediate ${\mathbb{S}}_2^L\times {\mathbb{S}}_2^R$ symmetry among the first two generations to regulate the sequential hierarchies, followed by random perturbations, that generate the correct size of all measured observables. Unique predictions for neutrinoless double beta decay are also found.

16 pages, 17 figures

References in corpus (12)

• The Unique Horizontal Symmetry of Leptons
• The Horizontal Symmetry for Neutrino Mixing
• Z_2 Symmetry Prediction for the Leptonic Dirac CP Phase
• Discrete symmetries and model-independent patterns of lepton mixing
• Neutrino Mass Sum-rules in Flavor Symmetry Models
• Classification of lepton mixing matrices from finite residual symmetries
• The $S_3$ flavour symmetry: Neutrino masses and mixings
• Broken S3 Symmetry in the Neutrino Mass Matrix and Non-Zero theta_{13}
• The breaking of flavor democracy in the quark sector
• Naturally perturbed S${}_3$ neutrinos
• Broken $S_{3\mathrm{L}}^{}\times S_{3\mathrm{R}}^{}$ Flavor Symmetry and Leptonic CP Violation
• Instanton Triggered Chiral Symmetry Breaking, the U(1) Problem and a Possible Solution to the Strong CP Problem