Minimal Froggatt-Nielsen Textures

TL;DR

This paper develops a method linking Froggatt-Nielsen charge assignments directly to quark masses and mixing angles, identifying minimal textures with charges not exceeding one, and analyzing their naturalness and tuning.

Contribution

It introduces a direct approach connecting FN charges to flavor observables and identifies minimal viable textures with low charges, enhancing understanding of the flavor puzzle.

Findings

Viable FN textures with charges ≤ 1 found

Most solutions do not require fine-tuning or cancellations

Provides a natural explanation for quark flavor structure

Abstract

The flavour problem of the Standard Model can be addressed through the Froggatt-Nielsen (FN) mechanism. In this work, we develop an approach to the study of FN textures building a direct link between FN-charge assignments and the measured masses and mixing angles via unitary transformations in flavour space. We specifically focus on the quark sector to identify the most economic FN models able to provide a dynamical and natural understanding of the flavour puzzle. Remarkably, we find viable FN textures, involving charges under the horizontal symmetry that do not exceed one in absolute value (in units of the flavon charge). Within our approach, we also explore the degree of tuning of FN models in solving the flavour problem via a measure analogous to the Barbieri-Giudice one. We find that most of the solutions do not involve peculiar cancellations in flavour space.