The Echo 12-23 Texture: A Novel Flavour Paradigm for Neutrinos

TL;DR

The paper presents a flavour-driven Type-I+II seesaw model with an $A_4\times Z_3\times Z_{10}$ symmetry that generates a distinctive Echo 12–23 texture in the Majorana neutrino mass matrix $M_\nu$, while keeping the charged-lepton sector diagonal and hierarchically structured. It reduces the neutrino sector to three real texture parameters, predicts a normal mass ordering with a quasi-degenerate spectrum and tightly constrained CP phases, and yields testable predictions for $0\nu\beta\beta$ decay, $\mu\to e\gamma$, and the CP asymmetry $A_{\mu e}$ in upcoming experiments. The model links high-scale flavon vevs to low-energy observables, offering precise correlations among $m_i$, $\delta$, $\alpha$, $\beta$, and $m_{\beta\beta}$, and provides a concrete framework to probe lepton flavour dynamics through future experimental data. The Appendix ensures the scalar potential vacuum alignment is stable by analytic and numerical checks of the Hessian, underpinning the robustness of the proposed texture realization.

Abstract

We construct a flavour guided model that realises the distinctive Echo 12-23 Texture in the neutrino mass matrix through a non-trivial interplay of symmetries. While the model accounts for charged lepton mass hierarchy, the texture offers interesting insights specifically into neutrino mass ordering and flavour dynamics. With clear imprints on low energy observables, the framework provides a minimal yet testable path toward understanding the origin of neutrino properties.

Figures (9)

• Figure 1: Feynman diagrams for Type-I and Type-II seesaw mechanisms.
• Figure 2: The plots of the predicted parameters are shown. (a) $\delta$ vs $\sum m_i$. (b) $m_{2,1}$ vs $m_3$. (c) $m_2-m_1$ vs $m_1$. (d) $\alpha$ vs $\beta$. (e) $\delta$ vs $J_{\text{CP}}$.
• Figure 3: The plots of the free parameters are shown. (a)$Im[s]$ vs $Re[s]$. (b) $Im[s]$ vs $Re[t]$.
• Figure 4: The plots of the model parameter combinations are shown.
• Figure 5: Feynman diagram for $0\nu\beta\beta$ decay.