Texture zeros and hierarchical masses from flavour (mis)alignment

TL;DR

This paper proposes a basis-independent approach to fermion mass matrices using invariants, revealing new insights into texture zeros and hierarchical structures through the concepts of alignment and misalignment.

Contribution

It introduces a novel parametrization of mass matrices based on basis-invariant trace, linking texture zeros and hierarchies to geometric alignments in flavor space.

Findings

Basis-invariant trace relates to mass matrix geometry.

Texture zeros correspond to specific alignments.

Misalignment explains Froggatt-Nielsen hierarchies.

Abstract

We introduce an unconventional interpretation of the fermion mass matrix elements. As the full rotational freedom of the gauge-kinetic terms renders a set of infinite bases called weak bases, basis-dependent structures as mass matrices are unphysical. Matrix invariants, on the other hand, provide a set of basis-independent objects which are of more relevance. We employ one of these invariants to give a new parametrization of the mass matrices. By virtue of it, one gains control over its implicit implications on several mass matrix structures. The key element is the trace invariant which resembles the equation of a hypersphere with a radius equal to the Frobenius norm of the mass matrix. With the concepts of alignment or misalignment we can identify texture zeros with certain alignments whereas Froggatt-Nielsen structures in the matrix elements are governed by misalignment. This method allows further insights of traditional approaches to the underlying flavour geometry.