Analytical solution for the correlator with Gribov propagators

Abstract

The propagators approximated by a meromorphic functions with complex conjugated poles are widely used to model infrared behaviour of QCD Green's functions. In this paper, the analytical solutions for a correlators 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 propagators has been considered as well. The result is different from the naive analytical continuation of the correlator primarily defined in the Euclidean space. For instance it is free of the ultraviolet divergences, even when the propagator has usual perturbative ultraviolet asymptotic \(\simeq 1/p^2\).