Gauge-invariant field strength correlations in QCD at zero and non-zero temperature

Abstract

We determine, by numerical simulations on a lattice, the gauge-invariant two-point correlation functions of the gauge field strengths in the QCD vacuum at zero temperature, down to a distance of 0.1 fm. We also study the behaviour of the gauge-invariant field correlators in the theory at finite temperature, across the deconfinement phase transition

On the dependence of the gauge-invariant field-strength correlators in QCD on the shape of the Schwinger string

“…At this value of β scaling has been already tested for the case of the straight-line paths in Refs. [17,18]. The data of Refs.…”

“…(2.4) and (2.5), we shall make use of the cooling technique, described in previous papers (see Refs. [20,21] and [17,18,19]). Cooling is a local procedure, which affects correlations at distances that grow as the square root of the number of cooling steps, as in a diffusion process.…”

“…(1.1) and (1.2) is assumed to be the straight line connecting the points 0 and x. Lattice data [16,17,18,19], which are the input for these SVM calculations, also refer to the choice of the straight-line parallel transport. With this choice the Schwinger string (1.2) reads:…”

“…Then, in the Euclidean region, translational, O(4)-and parity invariance require the correlator (1.1) to be of the following form [4,5,6]: The functions D(x 2 ) and D 1 (x 2 ) have been directly determined by numerical simulations on a lattice in the quenched (i.e., pure-gauge) theory, with gauge group SU(2) [16], in the quenched SU(3) theory in the range of physical distances between 0.1 and 1 fm [17,18] and also in full QCD, i.e., including the effects of dynamical fermions [19].…”

Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

“…Recalling from Eq. (4.47) that ζ ∼ 1/aE, and that the vacuum correlation length is of the order of a ∼ 0.2 ÷ 0.3 fm ∼ 1 ÷ 1.5 GeV −1 [64,65,66,67,68,69], we can estimate 49) which is less than one in the considered range of t and for not too heavy mesons. This estimate is quite conservative, and actually we expect that the typical transverse momentum of a parton involved in the process is of the same order of √ −t: for very small transferred momentum √ −t ≪ 1 GeV, we expect therefore that we can neglect the terms involving the transverse momentum of the partons, at least in a first approximation, so that the "contracted spin factors" are independent of ζ.…”