Exploring correlations in the stochastic Yang-Mills vacuum

TL;DR

This paper analytically evaluates correlation lengths in the stochastic Yang-Mills vacuum using path integrals, confirming previous Hamiltonian results and analyzing the behavior of nonconfining field correlations.

Contribution

It provides a direct analytic calculation of correlation lengths in the stochastic Yang-Mills vacuum, aligning with earlier Hamiltonian approaches and exploring the impact of path deviations.

Findings

Correlation lengths agree with previous Hamiltonian results.

Nonperturbative-nonconfining correlations decrease with path deviation.

Analytic path-integral method effectively evaluates Green functions.

Abstract

The correlation lengths of nonperturbative-nonconfining and confining stochastic background Yang-Mills fields are obtained by means of a direct analytic path-integral evaluation of the Green functions of the so-called one- and two-gluon gluelumps. Numerically, these lengths turn out to be in a good agreement with those known from the earlier, Hamiltonian, treatment of such Green functions. It is also demonstrated that the correlation function of nonperturbative-nonconfining fields decreases with the deviation of the path in this correlation function from the straight-line one.