Perturbative Static Four-Quark Potentials

A first attempt to understand hadron dynamics at low energies in terms of the fundamental quark and gluon degrees of freedom incorporates the 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 between static quarks, i.e.\ a generalization of the Wilson loop will be discussed. Making a connection with recent Monte Carlo lattice simulations for the lowest two energies of a system of two quarks and two antiquarks, the static $qq\bar{q}\bar{q}$-potential will be calculated in perturbation theory to fourth order. The result will be shown to be exactly equal to the prediction of a straightforward two-body approach, which in Monte Carlo lattice simulations has been found to be a reasonable approximation for very small interquark distances.