Quark-lepton compositeness: a three-body scenario

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 =σμv(1)σvλ(2)σλμ(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