Mass-gap equations within the QED framework: I

Abstract

The author introduces a substructure into the fermion lines of QED Feynman diagrams and find a substantial modification of the running coupling alpha (q2) at energies larger than the substructure mass scale ( Lambda ). The Feldman-Landau ghost vanishes if the number of light charged lepton states has an upper bound. Estimates of this bound are given; an ultraviolet fixed point appears. He applies these results to the radiative generation of charged lepton masses. This mechanism for the generation of fermion masses is analogous to the Schwinger mechanism in the boson sector or to the energy-gap generation in a superconductor. The masses arise non-perturbatively from the self-interaction of radial excitations of a massless bound state with the photon. Correspondingly, the bare masses are assumed to be zero. The coefficients of the resulting mass-gap equations depend on the magnitude of the ultraviolet fixed point. Only the case of asymptotic freedom can give rise to the right behaviour of the coefficients. The masses, obtained numerically, are indeed of the observed order of magnitude. In addition, the mass ratios of the first few states become largely similar to the observed values. That asymptotic freedom behaviour may be due to some kind of grand unification at energies Lambda approximately=1015 GeV; the properties of the heavy hypercolour states are of substantial significance for the whole light mass spectrum. The nondiagonal mass matrix elements are estimated and the effect of diagonalization of the mass matrix is analysed. It does not account for the large electron-muon mass ratio. He discovers that the diagonalization can lead to negative mass roots which sets an upper and physically relevant bound on alpha u, the value of alpha (q2) at q2 approximately= Lambda 2. The paper constitutes a nice example for the case where the desert hypothesis within the standard model does not hold.