Algebraic Approach to the Hypercoulomb Problem

The low-lying states of baryons are thought to be mainly composed of three-quarks configurations. Although for light (u,d) quarks a construction of the quark-quark interaction is very difficult, it has been suggested that a good fraction of this interaction is of three-body character [1], and that, in addition, it can be well approximated by a hypercentral potential, i.e. an interaction that is invariant under rotations in the six dimensional space spanned by the intrinsic coordinates of the three-body problem. This suggestion arose from a study of the flux tube configurations of Fig. 1 for heavy-quark baryons. However, in general, the fact that QCD is a non-abelian gauge theory leads to gluon-gluon couplings which, in turn, produce three-body forces, as shown in Fig. 2. One is thus led to the conclusion that three-body forces can be a very important part of the quark interactions and this is particularly so for baryons composed of light quarks where the coupling constant α_s is large.