PERTURBATIVE STATIC 4-QUARK POTENTIALS

A first attempt to understand hadron dynamics at low energies in terms of the fundamental quark and gluon degrees of freedom incorporates th e effects of the gluonic field into a potential depending only on the spatial positions of the quarks, which are considered in the infinite mass limit. A suitable framework for calculating such potentials betwe en static quarks, i.e. a generalization of the Wilson loop will be dis cussed. Making a connection with recent Monte Carlo lattice simulation s for the lowest two energies of a system of two quarks and two antiqu arks, the static qq(q) over bar (q) over bar-potential will be calcula ted in perturbation theory to fourth order. The result will be shown t o be exactly equal to the prediction of a straightforward two-body app roach, which in Monte Carlo lattice simulations has been found to be a reasonable approximation for very small interquark distances.