Charged Lepton Mass Spectrum and a Scalar Potential Model

TL;DR

This paper explores a scalar potential model for charged lepton masses, deriving relations among eigenvalues without relying on specific flavor symmetries, inspired by Sumino's recent work.

Contribution

It proposes a form of the scalar potential $V(\

Findings

Derived a general relation among eigenvalues of the scalar field $\

Proposed a scalar potential form that fits observed lepton mass spectrum.

Established a framework independent of explicit flavor symmetry models.

Abstract

Stimulated by a recent work by Sumino, on the basis of a model in which effective Yukawa coupling constants are described by vacuum expectation values of a scalar $\Phi$ with $3\times 3$ components, a possible form of the scalar potential $V(\Phi)$ which can well describe the observed charged lepton mass spectrum is investigated without referring to a specific flavor symmetry model. A general relation among eigenvalues of <\Phi> is derived without referring to an explicit form of $V(\Phi)$.