To what Distances do we know the Confining Potential?

Abstract

We argue that the commonly used procedure of extracting the static potential from lattice Wilson loop measurements may contain an underestimated systematic uncertainty at large quark separations. To illustrate the point, we extract the potential by the standard lattice method in a model vacuum made of instantons. A beautiful infinitely rising linear potential is obtained in the case where the true potential is in fact flattening. We argue that the flux tube formation might also be an artifact of the lattice procedure and not necessarily a measured physical effect. We conclude that at present the rising potential is known for sure up to no more than about 0.7 fm. It may explain why no screening has been clearly observed so far for adjoint sources or for fundamental sources but with dynamical fermions. Finally, we speculate on how confinement could be achieved despite the absense of the infinitely rising potential in the pure glue theory.