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

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.

💡 Research Summary

The fundamental mystery of neutrino physics lies in the origin of neutrino masses and the specific patterns of lepton flavor mixing. While neutrino oscillation experiments have definitively proven that neutrinos are massive and that flavors mix, the underlying mechanism governing the observed mass hierarchy and mixing angles remains one of the most significant challenges in particle physics. This paper addresses this “flavor problem” by proposing a structured symmetry-breaking scheme based on the $S_{3L} \times S_{3R}$ flavor symmetry.

The authors introduce a hierarchical breaking process, $S_{3L} \times S_{3R} \rightarrow S_{2L} \times S_{2R} \rightarrow \emptyset$, applied systematically to the mass matrices of both the charged-lepton and neutrino sectors. By investigating three distinct residual subgroups—$S_{2L}^{(23)} \times S_{2R}^{(23)}$, $S_{2L}^{(13)} \times S_{2R}^{(13)}$, and $S_{2L}^{(12)} \times S_{2R}^{(12)}$—the researchers performed a rigorous analysis of various mass matrix parameterizations.

The study’s primary strength lies in its quantitative alignment with experimental reality. Using the latest best-fit values for neutrino oscillation parameters, the paper predicts the Dirac CP-violating phase ($\delta$) to be $294.6^\circ$, $302.3^\circ$, and $287.0^\circ$ for the three respective scenarios. To ensure the robustness of these predictions, a comprehensive numerical analysis was conducted at the $3\sigma$ confidence level. The results demonstrate that the predicted ranges for $\delta$ (e.g., $282.7^\circ \rightarrow 297.0^\circ$ for one scenario) fall entirely within the experimentally allowed $3\sigma$ intervals.

In conclusion, the proposed $S_{3L} \times S_{3R}$ symmetry-breaking scheme provides a natural and mathematically elegant explanation for the observed lepton mass hierarchy and mixing patterns. By providing specific, testable predictions for the CP-violating phase that are consistent with current global fits, this work offers a highly valuable theoretical framework for future neutrino oscillation experiments and contributes significantly to our understanding of the fundamental symmetries of the universe.