Fermion Masses and Mixings from a Minimum Principle

TL;DR

This paper explores how fermion masses and mixings can be derived from a minimum principle applied to a flavor-invariant potential, revealing natural hierarchies and mixing patterns in leptons and neutrinos.

Contribution

It introduces a novel approach using a minimum principle on a flavor symmetry-invariant potential to explain fermion mass hierarchies and mixing angles, especially in the lepton sector.

Findings

Hierarchical charged lepton masses with degenerate Majorana neutrinos

One neutrino mixing angle close to maximal, another potentially large

Testable predictions for neutrino-less double beta decay and cosmology

Abstract

We analyze the structure of quark and lepton mass matrices under the hypothesis that they are determined from a minimum principle applied to a generic potential invariant under the $\left[U(3)\right]^5\otimes {\mathcal O}(3)$ flavor symmetry, acting on Standard Model fermions and right-handed neutrinos. Unlike the quark case, we show that hierarchical masses for charged leptons are naturally accompanied by degenerate Majorana neutrinos with one mixing angle close to maximal, a second potentially large, a third one necessarily small, and one maximal relative Majorana phase. The scheme presented here could be tested in the near future via neutrino-less double beta decay and cosmological measurements.