Boundary conditions for a composite model of leptons and quarks

Abstract

Because the existence of families of elements and hadrons was ultimately understood by the realization that atoms and hadrons are composite, an obvious approach to explaining the existence of lepton and quark families is to assume that the particles in these families are also composite. The mass and spin spectra of leptons and quarks suggest that if these particles are composite, they are most likely bound states of a scalar and spin-1/2 fermion interacting via electrodynamics. However, if they are composite, the bound states must be highly relativistic since in each family the least massive member has a small mass compared with the others. Also, composite leptons and quarks must be extremely tightly bound since no internal structure has ever been conclusively detected. Highly relativistic, bound-state, Bethe- Salpeter solutions of a scalar and a spin-1/2 fermion bound by minimal electrodynamics are discussed. These specific solutions cannot describe leptons or quarks as bound states because the magnitude of the charges of the constituents are an order of magnitude larger than e. The boundary conditions, however, allow solutions when the constituents have charges with magnitudes on the order of e.