A modified version of the Koide formula from flavor nonets in a scalar potential model and in a Yukawaon model

TL;DR

This paper introduces a modified Koide formula derived from scalar potential and Yukawaon models using SU(3) flavor symmetry, providing a natural explanation for fermion mass hierarchies in the Standard Model.

Contribution

It proposes a new version of the Koide formula based on scalar fields in nonet representations, fitting experimental fermion mass data with a natural theoretical framework.

Findings

Successfully fits charged lepton, up quark, and down quark mass data

Provides a theoretical basis for fermion mass spectrum

Involves invariant scalar potential and superpotential constructions

Abstract

We present a modified version of the Koide formula from a scalar potential model or from a Yukawaon model, based on scalar fields set up in a nonet representation of the SU(3) flavor symmetry in the Standard Model. The Koide's character, which involves the Standard Model fermion mass ratios, is derived from the vacuum expectation value of the nonet field in either model. The scalar potential in the scalar potential model or the superpotential in the Yukawaon model is constructed with all terms invariant under symmetries. The resulting Koide's character, which is modified by two effective parameters, can fit the experimental mass data of charged leptons, up quarks and down quarks. It offers a natural interpretation of the Standard Model fermion mass spectrum.