Partial mass-degeneracy and spontaneous CP violation in the lepton sector

TL;DR

This paper proposes models based on partial mass degeneracy and discrete flavor symmetries to explain fermion masses and mixings, successfully fitting experimental data and making testable predictions for future experiments.

Contribution

It introduces simple lepton sector models utilizing $D_N$ symmetry to reproduce observed data without unnatural hierarchies, highlighting the role of $Z_2$ subgroup in small electron mass and mixing angles.

Findings

Models fit experimental neutrino data well.

The $Z_2$ subgroup explains small electron mass and $ heta_{13}^{ m PMNS}$.

Predictions for neutrinoless-double-beta-decay and cosmology tests.

Abstract

Inspired by the small mass-squared difference measured in the solar neutrino oscillation experiments and by the testability, we suggest that a limit of the partial mass degeneracy, in which masses of the first two generation fermions are degenerate, may be a good starting point for understanding the observed fermion mass spectra and mixing patterns. The limit indicates the existence of a two-dimensional rotation symmetry, such as $O(2)$, $D_N$ and so on, in flavor space of the first two generations. We propose simple models for the lepton sector based on $D_N$ and show that the models can successfully reproduce the experimental data without imposing unnatural hierarchies among dimensionless couplings, although at least $10\%$ tuning is necessary in order to explain a large atmospheric mixing. It is especially found that the $Z_2$ subgroup of the $D_N$ symmetry plays an important role in understanding the smallness of the electron mass and $\theta_{13}^{\rm PMNS}$. We also discuss testability of the models by the future neutrinoless-double-beta-decay experiments and cosmological observations.