Lepton mass textures from non-invertible multiplication rules

TL;DR

This paper explores how gauging discrete symmetries affects lepton mass textures, revealing limitations and potential for realistic neutrino mass patterns beyond traditional group symmetries.

Contribution

It introduces a novel approach using non-invertible multiplication rules from gauged discrete symmetries to derive lepton mass textures, expanding beyond conventional group-theoretical methods.

Findings

Various charged lepton Yukawa textures are achievable.

Neutrino mass matrix patterns are limited by this approach.

Some textures can produce realistic neutrino masses.

Abstract

We study the lepton mass textures, which are derived by $\mathbb{Z}_2$ gauging of $\mathbb{Z}_M$ symmetries. We can obtain various textures for the Yukawa couplings in the charged lepton sector, but the patterns of neutrino mass matrices are limited. All the obtained textures can not be realized by group-theoretical symmetries, and certain textures can lead to realistic results.