A short-distance quark-antiquark potential

Abstract

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.We consider the static quark-antiquark potential in the background perturbation theory (BPT) [3]. 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 [4].2. The gluon field A µ in BPT is divided into the dynamical perturbative part a µ and the background nonperturbative field 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 [3] W (B + a) = W (B) + ∞ n=1

Novel solutions of RG equations for α(s) and β(α) in the large-N c limit

“…As it was shown in [2,3] the Background Perturbation Theory (BPT) is free of these defects and the coupling constant α B of BPT displays an important property of IR freezing (saturation) with α B (Q 2 = 0) ≈ 0.5 [2,3]. This behaviour of α B is well confirmed by experimental data on spin splitting of quarkonia levels [4,5] and by lattice data [6].…”

“…Consider e.g. the process e + e − into hadrons, and the photon self-energy part Π(Q 2 ), which has a pole expansion [3]…”

The gluonic condensate from the hyperfine splitting M cog(XcJ) — M(h c) in charmonium

“…Just due to the cancellation between the negative perturbative contribution and the positive NP one, the value ∆ HF (1P, cc) ∼ = −1 MeV has been calculated in [6] for a value of the gluonic condensate G 2 ∼ = 0.042 GeV 4 , while in Ref. [7] the same HF splitting has been obtained for the significantly smaller value G 2 ≈ 0.02 GeV 4 . The reason behind this difference will be explained below and comes from the fact that the gluonic condensate actually enters ∆ NP HF (1P ) in the combination G 2 T 2 g (T g is the gluonic correlation length) and therefore the extracted value of G 2 depends also on the correlation length T g used.…”

“…Spin-dependent NP potentials have been introduced in [14,15]. With the use of the vacuum correlation function (v.c.f.)…”

Static potential in baryon

“…Note that for mesons situation differs. The slope of the nonperturbative static potential in mesons almost does not change at small distances due to the interference with the perturbative fields [14].…”