Scheme variations of the QCD coupling and tau decays

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.

Comments: 4 pages, 3 figures. Contribution to "The 14th International Workshop on Tau Lepton Physics", 19--23 September 2016, IHEP, Beijing, China