A short distance quark - antiquark potential

Leading terms of the static quark-antiquark potential in the background perturbation theory are reviewed, including perturbative, nonperturbative and interference ones. The potential is shown to describe lattice data at short quark-antiquark separations with a good accuracy. 1. The static quark-antiquark potential was calculated with high accuracy in lattice QCD some years ago [1]. It was shown to be well described by the phenomenological Coulomb+linear Cornell potential at sufficiently large quark-antiquark separations, R > ∼ 0.2 fm. At smaller distances the Cornell potential is not applicable. The region 0.03 fm ≤ R ≤ 0.22 fm was studied in quenched lattice theory in detail [2], and the conclusion was made that the standard perturbative theory expansion in coupling constant does not yield appropriate description of lattice results, at least in one-and two-loop approximations. As is known, next terms of the asymptotic coupling expansion depend on the renormalization scheme, and so the corresponding static potential does. One can argue that the standard perturbative theory fails because this region is close to the unphysical Landau pole of the strong coupling. There is a wealth of literature on the short distance potential behavior, see [3], [4], [5], [6] and references therein. In the talk we consider the static quark-antiquark potential in the background perturbation theory (BPT) [7]. This potential incorporates both the features of the standard perturbative potential at tiny distances, R < ∼ 0.05 fm, and of the Cornell potential at R > ∼ 0.4 fm due to taking nonperturbative background field effects into account. After brief review of leading background potential terms we present our results concerning the behavior of the potential at short distances and its comparison with the lattice [5]. 2. The gluon field A µ in BPT is divided into the dynamical perturbative part a µ and the background nonperturbative field B µ , A µ = a µ + B µ. The background field, in which perturbative valence gluons propagate, results in the vacuum condensate creation. The static potential has to be calculated using the vacuum averaged Wilson loop for the quark-antiquark pair. The BPT Wilson loop expansion in the field a µ has the form [7]