Hyperasymptotics and quark-hadron duality violations in QCD

TL;DR

This paper explores the origins of quark-hadron duality violations in QCD by applying hyperasymptotic methods to analyze the two-point vector correlation function and its analytic continuation from Euclidean to Minkowski space.

Contribution

It introduces a hyperasymptotic approach to connect Borel plane singularities with duality violations and derives an expression for these violations at finite N_c based on Regge trajectory assumptions.

Findings

Established a link between Borel plane singularities and duality violations.

Derived an expression for duality violations at large but finite N_c.

Applied hyperasymptotics to analyze the operator product expansion in QCD.

Abstract

We investigate the origin of the quark-hadron duality-violating terms in the expansion of the QCD two-point vector correlation function at large energies in the complex $q^2$ plane. Starting from the dispersive representation for the associated polarization, the analytic continuation of the operator product expansion from the Euclidean to the Minkowski region is performed by means of a generalized Borel-Laplace transform, borrowing techniques from hyperasymptotics. We establish a connection between singularities in the Borel plane and quark-hadron duality violating contributions. Starting with the assumption that for QCD at $N_c=\infty$ the spectrum approaches a Regge trajectory at large energy, we obtain an expression for quark-hadron duality violations at large, but finite $N_c$.