Two-zero textures of the Majorana neutrino mass matrix from $\mathbb{Z}_3$ gauging of $\mathbb{Z}_N$ non-invertible symmetry

TL;DR

This paper explores how non-invertible $ ext{Z}_3$ gauging of $ ext{Z}_N$ symmetries can naturally produce specific two-zero Majorana neutrino mass textures, offering a predictive framework for neutrino mass models.

Contribution

It demonstrates that $ ext{Z}_3$ gauging of certain $ ext{Z}_N$ symmetries can realize all seven viable two-zero neutrino mass textures, expanding the understanding of symmetry origins of neutrino masses.

Findings

All seven viable two-zero textures can be generated from $ ext{Z}_3$ gauging of $ ext{Z}_{19}$.

Different neutrino mass generation mechanisms impose distinct symmetry constraints.

More general $ ext{Z}_n$ gauging introduces new fusion rules and richer structures.

Abstract

Texture-zero ansatze offer an economical description of neutrino masses, with current data allowing only seven inequivalent two-zero Majorana textures in the charged-lepton mass basis. We investigate how such textures can arise from non-invertible symmetries realized through $\mathbb{Z}_3$ gauging of $\mathbb{Z}_N$. In contrast to $\mathbb{Z}_2$ gauging, which necessarily induces diagonal neutrino mass terms via the Weinberg operator, $\mathbb{Z}_3$ gauging admits complex representations and allows a richer class of neutrino mass textures. If the light neutrino mass is described by the Weinberg operator, we find that the textures $\mathbf{A}_{1,2}$, $\mathbf{B}_{3,4}$, and $\mathbf{C}$ can be realized from the $\mathbb{Z}_{3}$ gauging of $\mathbb{Z}_{13}$ symmetry, while all the seven phenomenologically viable two-zero textures can emerge from $\mathbb{Z}_{3}$ gauging of $\mathbb{Z}_{19}$ symmetry without requiring supersymmetry. When the neutrino mass is generated by the type-I seesaw mechanism, the structure of the non-invertible symmetry is more restrictive, yielding only texture $\mathbf{C}$ for $N\neq7$. These results demonstrate the strong predictive power of non-invertible symmetries for neutrino mass textures. Furthermore, the more general $\mathbb{Z}_{n}$ gauging of the $\mathbb{Z}_{N}$ symmetry with $n>3$ is analyzed, which results in novel fusion rules.