Perturbative QCD relations inspired by hypothetical tau leptons

TL;DR

This paper reviews tests of perturbative QCD inspired by tau lepton decays, introducing scheme-independent relations and a method to measure the QCD Gell-Mann--Low Psi function, enhancing the understanding of strong interactions.

Contribution

It introduces scheme-independent commensurate scale relations for testing QCD predictions and proposes a new method to measure the QCD Gell-Mann--Low Psi function.

Findings

Validated the self-consistency of leading-twist QCD predictions

Developed a scheme-independent approach applicable over wide data ranges

Proposed a novel method to measure the QCD Gell-Mann--Low Psi function

Abstract

We review our recent works on tests of perturbative QCD, inspired by the relation between the hadronic decay of the tau lepton and the e+ e- annihilation into hadrons. First, we present a set of commensurate scale relations that probe the self-consistency of leading-twist QCD predictions for any observable which defines an effective charge. These tests are independent of the renormalization scheme and scale, and are applicable over wide data ranges. As an example we apply this approach to R_{e+ e-}. Second, using a differential form of these conmensurate scale relations, we present a method to measure the QCD Gell-Mann--Low Psi function.