Field correlator method for the confinement in QCD

The theory of confinement based on the stochastic field mechanism, known as the field correlator method (FCM) is discussed in detail. Experimental and lattice data have accumulated a vast amount of material on the properties of confinement in QCD. We enumerate all these properties as (1)–(7), and discuss beyond FCM two existing approaches: monopole based dual Ginzburg-Landau (DGL) theory, and Gribov-Zwanziger model, from this point of view. It is shown that the FCM satisfies all required criteria. We also prove its self-consistency; in particular, it is shown that the string tension $\sigma$ is the only scaleful parameter in the theory beyond fermion masses, and ${\mathrm{\Lambda }}_{\mathrm{QCD}}$ is calculated explicitly to the lowest order in terms of $\sigma$. We also formulate physical consequences of confinement, such as string breaking, Regge trajectories, role of confinement in the perturbation theory, chiral symmetry breaking, confinement in the boosted systems etc. It is demonstrated that the FCM is a suitable tool for the solution of these problems.

Figure 1

Calculation of the static potentials $V_D$, $V_1$ from field correlators.

Figure 2

The one-gluon gluelump Green’s function.

Figure 3

The two-gluon gluelump Green’s function.

Figure 4

The connected probe for measuring color field in the flux tube.

Figure 5

The transverse radius dependence of the CM current.

Figure 6

$E_3=E_3(r_{\perp },R=0.76\mathrm{fm})$. The transverse radius dependence of the CE field strength for the fixed flux tube length $R=0.76\mathrm{fm}$. The dots with error bars are from the lattice measurements in [42].

Figure 7

$E_3=E_3(r_{\perp },R=0.95\mathrm{fm})$. The transverse radius dependence of the CE field strength for the fixed flux tube length $R=0.95\mathrm{fm}$. The dots with error bars are from the lattice measurements in [42].

Figure 8

$E_3=E_3(r_{\perp },R=1.14\mathrm{fm})$. The transverse radius dependence of the CE field strength for the fixed flux tube length $R=1.14\mathrm{fm}$. The dots with error bars are from the lattice measurements in [42].

Figure 9

$E_3=E_3(r_{\perp },R=1.33\mathrm{fm})$. The transverse radius dependence of the CE field strength for the fixed flux tube length $R=1.33\mathrm{fm}$. The dots with error bars are from the lattice measurements in [39].

Figure 10

The minimal area surface for the gluon exchange interaction.

Figure 11

A distribution of the field ${\overrightarrow{E}}^{(B)}$ in GeV/fm with the only correlator $D$ contribution considered in the quark plane for equilateral triangle with the side 1 fm. Coordinates are given in fm, positions of quarks are marked by points.