A striking contradiction between lattice short range static potential (n f = 0) and standard perturbative potential, observed in Ref. [18], is investigated in the framework of the background perturbation theory. With the use of the background couplingα B (r) which contains the only background parameter -mass m B , fixed by fine structure fit in bottomonium, the lattice data are nicely explained without introduction of exotic short range linear potential with large "string tension" σ * ∼ 1 GeV 2 . A significant difference betweenα B (r) and standard perturbative vector coupling α V (r) is found in the range 0.05 fm < ∼ r < ∼ 0.15 fm, while at larger distances, r > 0.3 fmα B (r) fast approaches the freezing valueα B (∞). Some problems concerning the strong coupling properties at short and long distances are discussed and solutions are suggested. IntroductionThe property of freezing of the vector coupling constantα V (r) at long distances is widely used in QCD phenomenology [1]- [6]. On the fundamental level this phenomenon has been studied in two different theoretical approaches [7]-[9]. In the case of the static potential the freezing of the vector couplingα V (r) suggests thatα V (r) is approaching a constant α fr ≡α V (r → ∞) at relatively long distances while at small r it manifests the property of asymptotic freedom. Both characteristic features of the static potential were widely used in hadron spectroscopy. However, it was realized that the asymptotic freedom behavior does not practically affect hadron spectra being important mostly for a wave function at the origin. On the contrary, the choice ofα V (r) as a constant at all distances, i.e.α V (r) ∼ =ᾱ, appears to be a reasonable approximation and gives rise to a good description of meson spectra both for heavy quarkonia [1, 10, 11] and for heavy-light mesons [12]. Also in lattice QCD this choice gives a good fit to lattice static potential at the distances above 0.2 fm. Therefore the question arises why this simple approximation,α V (r) ≈ᾱ, works so well even in the case of bottomonium where the sizes of low-lying levels are not large, the characteristic radius R ch < ∼ 0.5 fm. To answer this question one needs to clarify another problem. Namely, to find out the precise freezing value of the vector constant in momentum and coordinate spaces, and to define the distances r where the difference betweenα V (r) and α fr is becoming inessential and therefore the approximationα V (r) =ᾱ (ᾱ = α fr in general case) gives a good description of hadron spectra and other physical characteristics.

Field distributions generated by static QQ and QQQ sources are calculated analytically in the framework of the Field Correlator Method (FCM) using Gaussian (bilocal) correlator. In both cases the string consists mostly of longitudinal color electric field, while transverse electric field contributes locally less then 3%, in agreement with earlier lattice studies. In the QQQ case the profile of the Y shape was calculated for the first time and found to have a complicated structure with a deep well at the string junction position. Possible consequences of this form for the baryon structure are discussed.

The short-and intermediate-distance behaviour of the hybrid adiabatic potentials is calculated in the framework of the QCD string model. The calculations are performed with the inclusion of Coulomb force. Spin-dependent force and the so-called string correction term are treated as perturbation at the leading potential-type regime. Reasonably good agreement with lattice measurements takes place for adiabatic curves excited with magnetic components of field strength correlators.

Gauge invariant extended configurations are considered for the three fundamental (quarks) or adjoint (gluons) particles. For quarks it is shown that the Y-shaped configuration is the only possible. For adjoint sources both the Y-shaped and triangular configurations may realize. The corresponding static potentials are calculated in the Method of Field Correlators and in the case of baryon shown to be consistent with the lattice simulations. For adjoint sources the potentials of Y-shaped and Delta-shaped configurations turn out to be close to each other, which leads to almost degenerate masses of 3-- 3g glueballs and odderon trajectories.Comment: 9 pages, 5 eps figures, latex2e, one reference adde

Field distributions generated by static QQ and QQQ sources are calculated analytically in the framework of Gaussian (bilocal) approximation of Field Correlator Method. Special attention is paid to the QQQ system and asymmetric configurations are also studied. At large quark separations fields form distinct stringlike shape. In both cases QQ and QQQ the string consists mainly of longitudinal color electric field. Transverse color electric component contribution is shown to be less then 3%. Baryon string has an Y -like shape with a deep well at the string junction position. Field distributions for quark-diquark and for three quarks on one line are considered. The interaction potential for quarks forming an equilateral triangle is calculated. The material of the paper is illustrated by 24 3D colored pictures.