Texture-zeros in minimal seesaw from non-invertible symmetry fusion rules

TL;DR

This work analyzes texture zeros in lepton mass matrices within a minimal seesaw framework by gauging a $Z_2$ outer automorphism of a $Z_N$ symmetry, producing non-invertible selection rules that constrain $Y_E$, $Y_ u$, $M_R$, and $M_ u$. It systematically classifies textures for $N=3,4,5$ and identifies maximal-zero patterns, including textures unattainable by conventional abelian symmetries, with detailed phenomenology for neutrino oscillations. In the diagonal and block-diagonal charged-lepton bases, it derives concrete predictions for zero entries in $M_ u$, relations among masses and mixings, and tight ranges for CP phases, offering testable targets for upcoming oscillation experiments. It further shows that higher $N$ can introduce new $Y_E$ textures (e.g., for $N=6,7,9$) but does not substantially enlarge the $Y_ u$ texture set, outlining a path toward more predictive textures in broader UV completions and GUT contexts.

Abstract

The $Z_2$ gauging of $Z_N$ symmetry can enforce certain elements of the fermion Yukawa couplings to vanish. We have performed a systematical study of texture zero patterns of lepton mass matrices in the minimal seesaw model, and we present all the possible patterns of the charged lepton Yukawa coupling $Y_E$, neutrino Yukawa coupling $Y_ν$, right-handed neutrino mass matrix $M_R$ and the light neutrino mass matrix $M_ν$ which can be derived from the $Z_2$ gauging of $Z_N$ symmetry. The realization of the textures with the maximum number of zeros and the second maximum number of zeros from non-invertible symmetry is studied, and the phenomenological implications in neutrino oscillation are discussed.

Figures (2)

• Figure 1: The contour plots of the texture zero constraint Eq. \ref{['eq:NO-io-m221/m231']} in the $\theta-\sigma$ plane for the NO neutrino masses. Five representative values $\delta_{CP}=124^{\circ}$, $168^{\circ}$, $212^{\circ}$, $288^{\circ}$, $364^{\circ}$ are shown in different colors, and the width of the lines arises from the $3\sigma$ uncertainty of $\frac{\Delta m^2_{21}}{\Delta m^2_{31}}$Esteban_2024.
• Figure 2: The contour plots of the texture zero constraint in Eq. \ref{['eq:NO-io-m221/m231']} in the $\theta-\sigma$ plane for the IO neutrino masses. Five representative values $\delta_{CP}=124^{\circ}$, $168^{\circ}$, $212^{\circ}$, $288^{\circ}$, $364^{\circ}$ are shown in different colors, and the width of the lines arises from the $3\sigma$ uncertainty of $\frac{\Delta m^2_{21}}{|\Delta m^2_{31}|}$Esteban_2024.