Scheme variations of the QCD coupling and tau decays

TL;DR

This paper introduces a scheme-invariant redefinition of the QCD coupling, enabling optimized predictions for tau decay processes and unifying scheme and scale variations.

Contribution

It proposes a new scheme parameterization of the QCD coupling, making its running scheme-independent and simplifying the analysis of scheme variations.

Findings

Scheme-independent running of the coupling $ ilde eta$ is achieved.

The $C$-scheme allows for optimized predictions of tau decay rates.

Preliminary results show potential for improved perturbative series analysis.

Abstract

The QCD coupling, $\alpha_s$, is not a physical observable since it depends on conventions related to the renormalization procedure. Here we discuss a redefinition of the coupling where changes of scheme are parametrised by a single parameter $C$. The new coupling is denoted $\hat \alpha_s$ and its running is scheme independent. Moreover, scheme variations become completely analogous to renormalization scale variations. We discuss how the coupling $\hat \alpha_s$ can be used in order to optimize predictions for the inclusive hadronic decays of the tau lepton. Preliminary investigations of the $C$-scheme in the presence of higher-order terms of the perturbative series are discussed here for the first time.