Analytic Reconstruction of heavy-quark two-point functions at O(\alpha_s^3)

TL;DR

This paper presents an analytic method to reconstruct heavy-quark two-point functions at order () using Mellin-Barnes transforms, combining multiple expansions for precise correlator analysis.

Contribution

It introduces a systematic Mellin-Barnes based reconstruction technique that integrates various expansions to improve heavy-quark correlator calculations.

Findings

Reconstruction accuracy improves with additional expansion terms

Method provides analytic control over correlator approximations

Applicable to vector, axial, scalar, pseudoscalar channels

Abstract

Using a method previously developed, based on the Mellin-Barnes transform, we reconstruct the two-point correlators in the vector, axial, scalar and pseudoscalar channels from the Taylor expansion at q^2=0, the threshold expansion at q^2=4m^2 and the OPE at q^2\rightarrow -\infty, where m is the heavy quark mass. The reconstruction is analytic and systematic and is controlled by an error function which becomes smaller as more terms in those expansions are known.