Fitting flavour symmetries: the case of two-zero neutrino mass textures

TL;DR

This paper introduces a numerical method for analyzing fermion mass matrices in flavor models, enabling efficient comparison with experimental data, stability analysis, and application to two-zero neutrino mass textures.

Contribution

The paper presents a novel numerical approach that simplifies the analysis of flavor model predictions without algebraic complexity, including a $$ comparison test and stability assessment.

Findings

Textures A1 and A2 are favored due to low  and compatibility with cosmological limits.

Allowed textures have constrained parameter spaces, some conflicting with cosmology.

Most forbidden textures remain forbidden, but some are sensitive to perturbations and could become allowed.

Abstract

We present a numeric method for the analysis of the fermion mass matrices predicted in flavour models. The method does not require any previous algebraic work, it offers a $\chi^{2}$ comparison test and an easy estimate of confidence intervals. It can also be used to study the stability of the results when the predictions are disturbed by small perturbations. We have applied the method to the case of two-zero neutrino mass textures using the latest available fits on neutrino oscillations, derived the available parameter space for each texture and compared them. Textures $A_{1}$ and $A_{2}$ seem favoured because they give a small $\chi^{2}$, allow for large regions in parameter space and give neutrino masses compatible with Cosmology limits. The other "allowed" textures remain allowed although with a very constrained parameter space, which, in some cases, could be in conflict with Cosmology. We have also revisited the "forbidden" textures and studied the stability of the results when the texture zeroes are not exact. Most of the forbidden textures remain forbidden, but textures $F_{1}$ and $F_{3}$ are particularly sensitive to small perturbations and could become allowed.