Unphysical properties of the static quark-antiquark four-point correlator in Landau gauge

We consider the four point connected correlator representing a static quark-antiquark pair separated by a spatial distance R, propagating for a Euclidean time T. This function is computed by lattice Monte Carlo in SU(2) pure gauge theory at lattice couplings $\beta=2.2$ and $\beta=2.5$ in both Coulomb and Landau gauges. The Coulomb gauge correlator is well behaved, and is dominated at large T by a state whose energy grows linearly as $\sigma R$, with $\sigma$ the known asymptotic string tension. The connected correlator in Landau gauge behaves differently. At intermediate R there is clear evidence of a linear potential, but the corresponding string tension extrapolates to zero at large T. At large R the connected correlator becomes negative; moreover there are strong finite size effects. These numerical results suggest that unphysical states dominate the large Euclidean time behavior of this Landau gauge correlator.