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 (me, mμ, mτ = (313.85773 MeV)[1 + √2 cos θk]2, 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 rk = ℓRe(1 + √2zk, in which the Kähler radial complex coordinate zk is a root of the Calabi-Yau condition z3 = exp(2i/3) for the envelopment of the particle surfaces and ℓ is a fundamental length constant. © World Scientific Publishing Company.