Reconstruction of heavy quark current correlators at O(\alpha_s^3)

TL;DR

This paper develops approximate formulas for high-order QCD contributions to various heavy quark current correlators, valid across all energy scales, using conformal mapping and Pade approximation techniques.

Contribution

It introduces a novel method combining conformal mapping and Pade approximation to estimate O(()) contributions for arbitrary momenta and masses in quark current correlators.

Findings

Provides approximate formulas valid for all energy scales.

Estimates unknown higher-order terms in expansions.

Enhances precision in theoretical predictions of quark correlators.

Abstract

We construct approximate formulas for the O(\alpha_s^3) QCD contributions to vector, axial-vector, scalar and pseudo-scalar quark current correlators, which are valid for arbitrary values of momenta and masses. The derivation is based on conformal mapping and the Pade approximation procedure and incorporates known expansions in the low energy, threshold and high energy regions. We use our results to estimate additional terms in these expansions.