Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Further study on the lepton mass spectra and flavor mixing with $S_{3L} \times S_{3R}$ flavor symmetry

Chang-Qi Hu, Chun-Yuan Li, Xiao Liang, Xing-Hua Yang, Dai-Xing Zhang

TL;DR

The paper addresses the challenge of explaining lepton mass spectra and flavor mixing by employing an $S_{3L} \times S_{3R}$ flavor symmetry with a two-stage breaking pattern $S_{3L} \times S_{3R} \rightarrow S_{2L} \times S_{2R} \rightarrow \emptyset$ applied to both charged-lepton and neutrino mass matrices. Nine parameters (four in the charged-lepton sector and five in the neutrino sector) are fixed by nine observables, enabling explicit predictions for the PMNS matrix and CP-violating phases. An analysis of three residual subgroups (23, 13, 12) yields distinct mass-matrix parameterizations, all compatible with current neutrino-oscillation data, including best-fit Dirac-phase values near $δ \approx 294.6^{\circ}$, $302.3^{\circ}$, and $287.0^{\circ}$, and $3\sigma$ ranges $281.2^{\circ} \rightarrow 338.7^{\circ}$, $287.0^{\circ} \rightarrow 342.2^{\circ}$, and $282.7^{\circ} ightarrow 297.0^{\circ}$. The model also predicts $\sum m_ν \approx 0.12$ eV and $\langle m \rangle_{ee} \approx 2.9 \times 10^{-2}$ eV, with Majorana phases close to trivial values. These results demonstrate that the symmetry-breaking scheme can naturally explain the lepton mass hierarchy and mixing, offering concrete, testable predictions for upcoming neutrino experiments and suggesting possible extensions to the quark sector.

Abstract

Neutrino oscillation experiments have confirmed that neutrinos are massive particles and lepton flavors are mixed. To explain the observed lepton mass spectra and flavor mixing patterns, flavor symmetry plays a crucial and unique role. In this paper, we propose a useful symmetry-breaking scheme by applying $S_{3L} \times S_{3R} \rightarrow S_{2L} \times S_{2R} \rightarrow \emptyset$ within both charged-lepton and neutrino sectors at the mass-matrix level. For the three distinct residual subgroups $S_{2L}^{(23)} \times S_{2R}^{(23)}$, $S_{2L}^{(13)} \times S_{2R}^{(13)}$ and $S_{2L}^{(12)} \times S_{2R}^{(12)}$ under consideration, we systematically analyze the various parameterizations of the lepton mass matrices. It is shown that all the three scenarios are in good agreement with current neutrino oscillation data. Notably, within the latest best-fit values of neutrino oscillation parameters, the predicted Dirac CP-violating phase $δ$ is calculated to be $294.6^\circ$, $302.3^\circ$ and $287.0^\circ$, respectively. To further assess the viability of the model, a comprehensive numerical analysis is performed by utilizing neutrino oscillation parameters at the $3σ$ level. It is found that the allowed range of $δ$ is $281.2^\circ \rightarrow 338.7^\circ$, $287.0^\circ \rightarrow 342.2^\circ$ and $282.7^\circ \rightarrow 297.0^\circ$, all fall within its $3σ$ range. These results indicate that the proposed symmetry-breaking scheme $S_{3L} \times S_{3R} \rightarrow S_{2L} \times S_{2R} \rightarrow \emptyset$ can naturally explain the realistic lepton mass hierarchy and mixing pattern, thereby providing valuable theoretical perspectives for future research.

Further study on the lepton mass spectra and flavor mixing with $S_{3L} \times S_{3R}$ flavor symmetry

TL;DR

The paper addresses the challenge of explaining lepton mass spectra and flavor mixing by employing an flavor symmetry with a two-stage breaking pattern applied to both charged-lepton and neutrino mass matrices. Nine parameters (four in the charged-lepton sector and five in the neutrino sector) are fixed by nine observables, enabling explicit predictions for the PMNS matrix and CP-violating phases. An analysis of three residual subgroups (23, 13, 12) yields distinct mass-matrix parameterizations, all compatible with current neutrino-oscillation data, including best-fit Dirac-phase values near , , and , and ranges , , and . The model also predicts eV and eV, with Majorana phases close to trivial values. These results demonstrate that the symmetry-breaking scheme can naturally explain the lepton mass hierarchy and mixing, offering concrete, testable predictions for upcoming neutrino experiments and suggesting possible extensions to the quark sector.

Abstract

Neutrino oscillation experiments have confirmed that neutrinos are massive particles and lepton flavors are mixed. To explain the observed lepton mass spectra and flavor mixing patterns, flavor symmetry plays a crucial and unique role. In this paper, we propose a useful symmetry-breaking scheme by applying within both charged-lepton and neutrino sectors at the mass-matrix level. For the three distinct residual subgroups , and under consideration, we systematically analyze the various parameterizations of the lepton mass matrices. It is shown that all the three scenarios are in good agreement with current neutrino oscillation data. Notably, within the latest best-fit values of neutrino oscillation parameters, the predicted Dirac CP-violating phase is calculated to be , and , respectively. To further assess the viability of the model, a comprehensive numerical analysis is performed by utilizing neutrino oscillation parameters at the level. It is found that the allowed range of is , and , all fall within its range. These results indicate that the proposed symmetry-breaking scheme can naturally explain the realistic lepton mass hierarchy and mixing pattern, thereby providing valuable theoretical perspectives for future research.

Paper Structure

This paper contains 8 sections, 57 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. $S_{3L} \times S_{3R}$ Flavor Symmetry Framework
  3. Lepton Mass Spectra and Mixing Matrix
  4. Scenario I ($S_{3L} \times S_{3R} \rightarrow S^{(23)}_{2L} \times S^{(23)}_{2R} \rightarrow \emptyset$)
  5. Scenario II ($S_{3L} \times S_{3R} \rightarrow S^{(13)}_{2L} \times S^{(13)}_{2R} \rightarrow \emptyset$)
  6. Scenario III ($S_{3L} \times S_{3R} \rightarrow S^{(12)}_{2L} \times S^{(12)}_{2R} \rightarrow \emptyset$)
  7. Numerical Analysis and Predictions for CP Violation
  8. Conclusion

Figures (1)

  • Figure 1: The predicted Dirac CP-violating phase $\delta$ as a function of $\sin^2\theta_{23}$ for (a) Scenario I, (b) Scenario II and (c) Scenario III.