The Structure of Flavor Mixing and Reconstruction of the Mass Matrix

TL;DR

This paper investigates the fermion flavor structure through mass matrix decomposition, proposing a minimal parameterization of flavor mixing, and reconstructs fermion mass matrices, revealing a natural emergence of flat matrices and insights into flavor breaking.

Contribution

It introduces a bilinear decomposition approach to fermion mass matrices, providing a minimal parameterization of flavor mixing with new phases and angles, and reconstructs mass matrices under hierarchy assumptions.

Findings

Flavor mixing can be treated independently.

A minimal parameterization with two phases and two angles is achieved.

A natural emergence of flat mass matrices from hierarchy considerations.

Abstract

The Fermion flavor structure is investigated by bilinear decomposition of the mass matrix after EW symmetry breaking, and the roles of factorized matrices in flavor mixing and mass generation are explored. It is shown that flavor mixing can be addressed as an independent issue. On a new Yukawa basis, the minimal parameterization of flavor mixing is realized containing two relative phases and two free $SO(2)_L$ rotation angles. The validity of the flavor mixing structure is checked in both the lepton and quark sectors. Under the decomposition of flavor mixing, fermion mass matrices are reconstructed under the hierarchy limit. A flat mass matrix with all elements equal to 1 arises naturally from the requirement that homology exists between up-type and down-type fermion mass matrices. Some hints of a flat matrix and flavor breaking are also discussed.