A new class of invariants in the lepton sector

TL;DR

This paper introduces a new set of basis-invariant combinations of lepton mass matrices, enabling basis-independent analysis of symmetries and textures in the lepton sector.

Contribution

It develops a novel class of invariants that facilitate basis-independent study of lepton mass textures and symmetries, including $$ exchange and reflection symmetries.

Findings

Invariants can express various flavor symmetries in a basis-independent manner.

The approach unifies the analysis of texture zeros and symmetries.

Provides tools for systematic exploration of lepton mass models.

Abstract

We construct a new set of combinations from the mass matrices of the charged leptons and neutrinos that are invariant under basis transformation, hereafter {\it the} invariants. We use these invariants to study various symmetries and neutrino mass textures in a basis independent way. In particular, we show that by using these invariants the ansatz such as $\mu-\tau$ exchange and reflection symmetries, various texture zeros and flavor symmetries can be expressed in a general basis.