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

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 $N\ne 7$. 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.

Comments: 39 pages, 1 figure