Analytic Approach to Perturbative QCD and Renormalization Scheme Dependence

TL;DR

This paper develops an analytic, ghost-free model for the QCD running coupling that reduces renormalization scheme dependence in the $e^+e^-$ annihilation cross-section calculations, especially at low energies.

Contribution

It introduces an analytized approach to QCD corrections up to three loops, demonstrating improved stability against scheme dependence in low-energy regimes.

Findings

The analytized model shows remarkable stability compared to conventional methods.

The approach effectively reduces scheme dependence in the low-energy region.

It extends the analytic ghost-free QCD coupling to practical processes like $e^+e^-$ annihilation.

Abstract

We further develop the approach recently used to construct an analytic ghost-free model for the QCD running coupling based on the requirement of the $Q^2$-analyticity and apply it to the process of $e^+e^-$ annihilation into hadrons to study the renormalization scheme dependence of the $R(s)$ cross-section ratio. \par By transforming the relevant QCD corrections up to the three-loop level into the "analytized" form we show that the $R_{AA}(s)$ expression thus obtained is remarkably stable (as compared to the conventional perturbative approach) with respect to the renormalization scheme dependence for the whole low-energy region.