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

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.

Comments: 17 pages. v2: The introduction is rewritten with a complete review. Section 2 and 3 are presented more clearly. v3: The distinction between mass singular values and eigenvalues is clarified. v4: Quark mass ratios excluding QCD renormalization factors are used to calculate the Koide's character for quarks in concluding remarks. Typos. Nucl.Phys.B pre-publication version