Quark-lepton compositeness: a three-body scenario

Abstract

The Harari-Shupe model of quarks and leptons is viewed, not as a gauge theory, but as a quantum-mechanical three-body problem of the extreme relativistic type involving massless preons. Considerations based on S³-symmetry in the available degrees of freedom (spin, isospin, space and hypercolour) are employed in conjunction with a spin-dependence ansatz on the three-preon forces (∑ ^a =σ_μv⁽¹⁾σ_vλ⁽²⁾σ_λμ⁽³⁾) for an understanding of the three basic issues of (i) spin-1/2, (ii) generation structure and (iii) steeply rising mass patterns of quark-lepton families. The ∑^a-dynamics is compatible with the interpretation of colour as a manifestation of S₃-symmetry, as envisaged in the original Harari-Shupe proposal, while the interpretation of the generation structure devolves on the role of a certain quantum number N which takes on three different classes of values (3n, 3n ± 1;n = 0, 1, 2, ...) according to the S₃-symmetry of the spatial wavefunction.