Algebraic Approach to Baryon Structure

Abstract

In the usual description of baryons in terms of three constituents, the wave-function is a product of a space part and an internal spin-flavor-color part. Algebraic methods have been used extensively in the past to describe the internal part in terms of the symmetry groups SU _sf (6)⊗SU _c (3) [1, 2]. The difference between models lies in different assumptions on the spatial dynamics of the three constituents. Quark potential models in nonrelativistic [3] or relativized [4] forms emphasize the single-particle aspects of quark dynamics for which only a few low-lying configurations in the confining potential contribute significantly to the eigenstates of the Hamiltonian. Excited baryons in this description correspond to single-particle excitations of levels in the confining potential. On the other hand, flux-tube models, soliton models as well as some regularities in the observed spectra (e.g. linear Regge trajectories, parity doubling) hint that an alternative, collective type of dynamics may play a role in the structure of baryons.