Analytical solution for the correlator with Gribov propagators

TL;DR

This paper derives analytical solutions for two-point correlators with complex conjugated poles in Minkowski space, including the Gribov propagator, revealing differences from Euclidean continuation and offering divergence-free results.

Contribution

It provides the first analytical solutions for correlators with complex conjugated poles in Minkowski space, including the Gribov propagator, advancing understanding of infrared QCD Green's functions.

Findings

Solutions are free of ultraviolet divergences.

Results differ from naive Euclidean continuation.

Correlators satisfy Gribov integral representation.

Abstract

Propagators approximated by a meromorphic functions with complex conjugated poles are widely used to model infrared behavior of QCD Green's functions. In this paper, analytical solutions for two point correlator made out of functions with complex conjugated poles or branch points have been obtained in the Minkowski space for the first time. As a special case the Gribov propagator has been considered as well. The result is different from the naive analytical continuation of the correlator primarily defined in the Euclidean space. It is free of ultraviolet divergences, and instead of Lehmann it rather satisfies Gribov integral representation.