Broken $S_{3\mathrm{L}}^{}\times S_{3\mathrm{R}}^{}$ Flavor Symmetry and Leptonic CP Violation

Abstract

In the framework of canonical seesaw model, we present a simple but viable scenario to explicitly break an $S_{3\mathrm{L}}^{}\times S_{3\mathrm{R}}^{}$ flavor symmetry in the leptonic sector. It turns out that the leptonic flavor mixing matrix is completely determined by the mass ratios of charged leptons (i.e., $m_e^{}/m_{\mu }^{}$ and $m_{\mu }^{}/m_{\tau }^{}$) and those of light neutrinos (i.e., $m_1^{}/m_2^{}$ and $m_2^{}/m_3^{}$). The latest global-fit results of three neutrino mixing angles $\{{\theta }_{12}^{},{\theta }_{13}^{},{\theta }_{23}^{}\}$ and two neutrino mass-squared differences $\{\Delta m_{21}^2,\Delta m_{31}^2\}$ at the $3\sigma$ level are used to constrain the parameter space of $\{m_1^{}/m_2^{},m_2^{}/m_3^{}\}$. The predictions for the mass spectrum and flavor mixing are highlighted: (1) The neutrino mass spectrum shows a hierarchical pattern and a normal ordering, e.g., $m_1^{}\approx 2.2\mathrm{meV}$, $m_2^{}\approx 8.8\mathrm{meV}$ and $m_3^{}\approx 52.7\mathrm{meV}$; (2) Only the first octant of ${\theta }_{23}^{}$ is allowed, namely, $41.8^{\circ }\lesssim {\theta }_{23}^{}\lesssim 43.3^{\circ }$; (3) The Dirac CP-violating phase $\delta \approx -22^{\circ }$ deviates significantly from the maximal value $-90^{\circ }$. All these predictions are ready to be tested in the ongoing and forthcoming neutrino oscillation experiments. Moreover, we demonstrate that the cosmological matter-antimatter asymmetry can be explained via resonant leptogenesis, including the individual lepton-flavor effects. In our scenario, the leptonic CP violation at low- and high-energy scales are closely connected.

23 pages, 4 figures, to be published in Chinese Physics C

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