Scheme variations of the QCD coupling and hadronic $\tau$ decays

TL;DR

This paper introduces a scheme-invariant definition of the QCD coupling, $ ilde\alpha_s$, which improves the perturbative predictions for processes like $e^+e^-$ scattering and $ au$ decays by reducing scheme dependence.

Contribution

It proposes a new renormalization scheme invariant QCD coupling, parameterized by a single variable, enhancing the accuracy of perturbative QCD predictions.

Findings

The new coupling reduces scheme dependence in QCD calculations.

Appropriate choices of the parameter $C$ improve perturbative predictions.

Application to $e^+e^-$ and $ au$ decay data shows better agreement with experiments.

Abstract

The Quantum Chromodynamics (QCD) coupling, $\alpha_s$, is not a physical observable of the theory since it depends on conventions related to the renormalization procedure. We introduce a definition of the QCD coupling, denoted by $\hat\alpha_s$, whose running is explicitly renormalization scheme invariant. The scheme dependence of the new coupling $\hat\alpha_s$ is parameterized by a single parameter $C$, related to transformations of the QCD scale $\Lambda$. It is demonstrated that appropriate choices of $C$ can lead to substantial improvements in the perturbative prediction of physical observables. As phenomenological applications, we study $e^+e^-$ scattering and decays of the $\tau$ lepton into hadrons, both being governed by the QCD Adler function.