Koide Lepton Relation Explained by Lepton Radius (Compton Wavelength)/4

Abstract

The intriguing Koide relation between lepton masses, , involving electron mass m e , muon mass m μ , and tau mass m t , was first presented in 1982. The reason why Q 1 ≈ 2/3 has long been unclear. However, describing Standard Model fermions as spheres with radius (Compton wavelength)/4, allows only three fermions in each charge state and avoids the infinite energy density of point particles. Then the Koide parameter Q 1 ≈ 2/3 because the electron Compton wavelength is more than 200 times the muon and tau Compton wavelengths. A tau mass equivalent of 1776.98 MeV, within experimental error bars, would result in Q 1 = 2/3. The analysis is discussed in the context of efforts to extend the Standard Model of particle physics.