Asymptotic power series of field correlators

TL;DR

This paper explores the ambiguity in reconstructing functions from their asymptotic power series expansions, using a modified Watson lemma to analyze functions represented by Laplace-Borel integrals, with potential applications in QCD.

Contribution

It introduces a modified Watson lemma to study the ambiguity of functions determined by asymptotic expansions and their integral representations in the Borel plane.

Findings

Identifies classes of functions sharing the same asymptotic expansion.

Provides a framework for analyzing ambiguities in Borel-Laplace integral representations.

Discusses potential applications in quantum chromodynamics (QCD).

Abstract

We address the problem of ambiguity of a function determined by an asymptotic perturbation expansion. Using a modified form of the Watson lemma recently proved elsewhere, we discuss a large class of functions determined by the same asymptotic power expansion and represented by various forms of integrals of the Laplace-Borel type along a general contour in the Borel complex plane. Some remarks on possible applications in QCD are made.