Higher-order behaviour of two-point current correlators

TL;DR

This paper investigates higher-order contributions to two-point current correlators in QCD, constructing models for their perturbative series that incorporate scheme choices and operator constraints, providing improved understanding of perturbative corrections.

Contribution

It introduces models for Borel transforms of perturbative series respecting QCD constraints and employs the $C$-scheme for the coupling, offering new insights especially for the scalar correlator.

Findings

Scalar correlator corrections are scheme-dependent and can be reduced in the $C$-scheme.

Supports previous results for the Adler function obtained in the $ar{MS}$ scheme.

Highlights the importance of scheme choice in perturbative QCD calculations.

Abstract

Estimates of higher-order contributions for perturbative series in QCD, in view of their asymptotic nature, are delicate, though indispensable for a reliable error assessment in phenomenological applications. In this work, the Adler function and the scalar correlator are investigated, and models for Borel transforms of their perturbative series are constructed, which respect general constraints from the operator product expansion and the renormalisation group. As a novel ingredient, the QCD coupling is employed in the so-called $C$-scheme, which has certain advantages. For the Adler function, previous results obtained directly in the $\overline{\rm MS}$ scheme are supported. Corresponding results for the scalar correlation function are new. It turns out that the substantially larger perturbative corrections for the scalar correlator in $\overline{\rm MS}$ are dominantly due to this scheme choice, and can be largely reduced through more appropriate renormalisation schemes, which are easy to realise in the $C$-scheme.