Saturation of confining forces in a relativistic quark model for the baryons

Abstract

A relativistic quark model for the baryons with saturating three-particle forces is investigated. The properties of relativistic three-fermion amplitudes are analyzed with respect to Lorentz transformations and permutations. Six different classes of possible structures in spin space are found. They serve as an appropriate basis for the classification and calculation of spin-dependent interactions. The quantum numbers and amplitudes for the orbital part are determined for Euclidean relative vectors with help of the irreducible representations of the groups SU(4) ⊃ SO(4) ⊃ SO(3). These kinematical results together with the Green's function techniques of relativistic quantum field theory are applied to a Bethe-Salpeter model for the binding of three heavy quarks inside a baryon. We give as an example a confining saturating interaction which yields baryon quantum numbers similar to those of the non-relativistic harmonic oscillator model. However, the spin structure of the amplitudes obtained in this way differs from the boosted non-relativistic ones. This feature is important, since the phenomenological discussion of photoproduction and strong decays of the baryon resonances shows that at least sizable corrections to the non-relativistic amplitudes are necessary.