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

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 $\delta$ 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 $3\sigma$ level. It is found that the allowed range of $\delta$ 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 $3\sigma$ 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.