U(3)-Flavor Nonet Scalar as an Origin of the Flavor Mass Spectra

TL;DR

This paper explores how a U(3)-flavor nonet scalar's VEV structure can explain the mass spectra of down quarks and charged leptons, proposing a model where flavor symmetry is fully broken without subgroups.

Contribution

It introduces a novel approach linking the VEVs of a U(3)-flavor nonet scalar to fermion mass spectra, without breaking the full U(3) symmetry.

Findings

Derived relations for lepton mass ratios using a toy model

Showed complete spontaneous breaking of U(3) flavor symmetry

Analyzed mass spectrum ratios based on VEV structures

Abstract

According to an idea that the quark and lepton mass spectra originate in a VEV structure of a U(3)-flavor nonet scalar \Phi, the mass spectra of the down-quarks and charged leptons are investigated. The U(3) flavor symmetry is spontaneously and completely broken by non-zero and non-degenerated VEVs of $\Phi$, without passing any subgroup of U(3). The ratios (m_e+m_\mu+m_\tau)/(\sqrt{m_e}+\sqrt{m_\mu}+\sqrt{m_\tau})^2 and \sqrt{m_e m_\mu m_\tau}/(\sqrt{m_e}+\sqrt{m_\mu}+\sqrt{m_\tau})^3 are investigated based on a toy model.