High precision study of the $Q\overline{Q}$ potential from Wilson loops at large distances

For lattice QCD with two sea quark flavors we study the static quark-antiquark potential $V\left(R\right)\mathrm{}$ in the regime where string breaking is expected. In order to increase the statistics, we make full use of the lattice information by including all lattice vectors $\mathbf{R}$ to any given separation $R=|\mathbf{R}|$ in the infrared regime. The corresponding paths between the lattice points are constructed by means of a generalized Bresenham algorithm as known from computer graphics. As a result, we achieve a determination of the Wilson loops in the range $0.8–1.5\hspace{0.5em}\mathrm{fm}$ with hitherto unknown precision. Finally, we discuss the impact of this approach on the signal of the transition matrix element between two- and four-quark states.