Weak Basis Transformations and Texture Zeros in the Leptonic Sector

TL;DR

This paper examines the physical significance of texture zeros in leptonic mass matrices, showing some are basis-dependent while others have physical implications, especially in four-zero texture models.

Contribution

It demonstrates that certain texture zeros are basis artifacts, while four-zero textures with identical charged lepton and neutrino matrices have physical meaning and can be classified into four distinct classes.

Findings

Some texture zeros are basis-dependent and lack physical content.

Four-zero texture Ansatze with identical charged lepton and neutrino matrices are physically meaningful.

These four-zero textures can be categorized into four classes with distinct implications.

Abstract

We investigate the physical meaning of some of the texture zeros which appear in most of the Ansatze on leptonic masses and their mixing. It is shown that starting from arbitrary lepton mass matrices and making suitable weak basis transformations one can obtain some of these sets of zeros, which therefore have no physical content. We then analyse four-zero texture Ansatze where the charged lepton and neutrino mass matrices have the same structure. The four texture zeros cannot be obtained simultaneously through weak basis transformations, so these Ansatze do have physical content. We show that they can be separated into four classes and study the physical implications of each class.