Static three-quark SU(3) and four-quark SU(4) potentials

Abstract

We present results on the static three- and four-quark potentials in SU(3) and SU(4), respectively, within quenched lattice QCD. We use an analytic multihit procedure for the time links and a variational approach to determine the ground state. The three- and four-quark potentials extracted are consistent with a sum of two-body potentials, possibly with a weak many-body component at larger distances. For quark separations up to $\ensuremath{\sim}1.2 \mathrm{fm}$ where the results are most accurate, we find support for the $\ensuremath{\Delta}$ Ansatz for the baryonic area law.