HEURISTIC DEVELOPMENT OF A DIRAC–GOLDHABER MODEL FOR LEPTON AND QUARK STRUCTURE

Abstract

All three charged lepton pole masses are given to O(10-5) accuracy by [Formula: see text], where θk = 2πk/3 + 2/9 with the generation number k = 1, 2, 3. In the context of a Dirac model, it is shown that this empirical formula for the charged leptons admits a satisfactory S3-parametrized extension for the scale-independent pole masses of quarks and Majorana neutrinos; in particular, the top quark mass emerges as 177.698 GeV. A physical-geometrical interpretation of the mass formula supports Dirac's and Goldhaber's proposals: leptons and quarks of the same generation are identical in size and shape. Specifically, their self-interaction mass appears to be concentrated on spherical surfaces of radii [Formula: see text], in which the Kähler radial complex coordinate zk is a root of the Calabi–Yau condition [Formula: see text] for the envelopment of the particle surfaces and ℓ is a fundamental length constant.