The mass ratios parametrization

TL;DR

This paper proposes a model-independent set of conditions to naturally explain fermion mass hierarchies and mixing, suggesting the existence of a flavor symmetry and providing testable predictions for neutrino masses.

Contribution

It introduces a novel set of conditions linking fermion mass ratios to mixing, offering a new perspective on flavor symmetry in the Standard Model.

Findings

Fermion mixing can be described by four independent mass ratios.

Application to the Standard Model explains quark and lepton mixing patterns.

Predicts a lower bound on the lightest neutrino mass, testable in future experiments.

Abstract

The observed hierarchy in the fermion masses, which imply a set of small mass ratios, is not naturally small regarding 't Hooft's criteria. In this work, in a model independent approach, we introduce a set of conditions by which fermion mass ratios become natural. Interestingly, these conditions demand that fermion mixing should be described by the four independent mass ratios of each fermion sector. Application of this set of conditions to the standard theory enables one to understand the mains aspects in quark and lepton mixing. This feature can be taken as a strong evidence for the existence in Nature of a flavour symmetry. Also, for this analysis to work in the lepton sector, neutrino masses should have normal ordering with the lightest neutrino mass satisfying the lower bound, $m_{\nu 1} \geqslant (5.0\pm 0.1) \text{ meV}$, making the approach testable.