Heuristic Development of a Dirac-Goldhaber Model for Lepton and Quark Structure

All three charged lepton pole masses are given to O(10^-5) accuracy by (m_e, m_{μ ,} m_{τ )=(313.85773} MeV)[1+√ {2} cos θ _k]², where θ_k = 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 r_k =l Re(1 +√ {2}z_k), in which the Kähler radial complex coordinate z_k is a root of the Calabi-Yau condition z^3=exp(˙ 2i/3) for the envelopment of the particle surfaces and ℓ is a fundamental length constant.