Flavor Hierarchy Quadratic Rule and Dual Quark-Neutrino Mixing Patterns

TL;DR

This paper introduces two semi-empirical rules that unify flavor hierarchies and mixing patterns of neutrinos, quarks, and charged leptons, revealing underlying regularities and a common small flavor parameter.

Contribution

It proposes the quadratic DMD-hierarchy and DMD-duality rules that connect neutrino and quark flavor structures and predict neutrino degeneracy from mass hierarchies.

Findings

Neutrino and quark mixing deviations are nearly equal in magnitude.

A single small parameter (~0.0067) describes flavor deviations.

The rules unify flavor hierarchies across different particle types.

Abstract

Flavor physics is about particle mass-degeneracy-deviations (DMD) and mixing and especially about hierarchies of those deviations. On the one hand there is no established theory of particle flavor at present; on the other hand there are growing data indications on interesting empirical flavor regularities that are described here by two semi-empirical rules: quadratic DMD-hierarchy and Dirac-Majorana DMD-duality rules. First rule unites neutrino solar-atmospheric hierarchy parameter with charged lepton (CL) and quark mass-ratio hierarchies and simultaneously unites the hierarchies in the mixing matrices of quarks and neutrinos; the second rule predicts quasi-degenerate neutrinos from the fact of CL and quark large mass hierarchy and explains quark-neutrino complementarity mixing relations. The neutrino and quark mixing data seem very different, but it results that small deviations from maximal neutrino mixing are nearly equal to the small deviations from minimal mixing of quarks. Those deviations are quantitatively described by only one new small flavor parameter ~0.0067.