New Origin of a Bilinear Mass Matrix Form

TL;DR

This paper proposes a new origin for the bilinear form of fermion mass matrices using a U(3) flavor symmetry and scalar field VEVs, providing a natural explanation for charged lepton masses.

Contribution

It introduces a novel mechanism where the bilinear Yukawa coupling form arises from scalar field VEVs without non-renormalizable interactions, under specific symmetry breaking conditions.

Findings

Yukawa couplings proportional to scalar VEV products

Natural explanation for charged lepton mass formula

Speculation on scalar field VEV structure

Abstract

The charged lepton mass formula can be explained when the masses are propotinal to the squared vacuum expectation values (VEVs) of scalar fields. We introduce U(3) flavor symmetry and its nonet scalar field $\Phi$, whose VEV structure plays an essential role for generating the fermion mass spectrum. We can naturally obtain bilinear form of the Yukawa coupling $Y_{ij} \propto \sum_k <\Phi_{ik}> <\Phi_{kj}>$ without the non-renormalizable interactions, when the flavor symmetry is broken only through the Yukawa coupling and tadpole terms. We also speculate the possible VEV structure of $<\Phi>$.