Can an unbroken flavour symmetry provide an approximate description of lepton masses and mixing?

TL;DR

This paper investigates whether unbroken flavour symmetries can approximate lepton masses and mixings, identifying six viable cases and highlighting the importance of symmetry breaking effects for certain neutrino spectra.

Contribution

It provides a complete classification of flavour groups and representations that approximate lepton masses and mixings in the symmetric limit, using a novel algorithm based on irreducible component decomposition.

Findings

Six viable cases of flavour representations identified

Neutrinos are either anarchical or have inverted hierarchy in these cases

In SU(5) unification, only the anarchical scenario is compatible

Abstract

We provide a complete answer to the following question: what are the flavour groups and representations providing, in the symmetric limit, an approximate description of lepton masses and mixings? We assume that neutrinos masses are described by the Weinberg operator. We show that the pattern of lepton masses and mixings only depends on the dimension, type (real, pseudoreal, complex), and equivalence of the irreducible components of the flavour representation, and we find only six viable cases. In all cases the neutrinos are either anarchical or have an inverted hierarchical spectrum. In the context of SU(5) unification, only the anarchical option is allowed. Therefore, if the hint of a normal hierarchical spectrum were confirmed, we would conclude (under the above assumption) that symmetry breaking effects must play a primary role in the understanding of neutrino flavour observables. In order to obtain the above results, we develop a simple algorithm to determine the form of the lepton masses and mixings directly from the structure of the decomposition of the flavour representation in irreducible components, without the need to specify the form of the lepton mass matrices.