Scheme variations of the QCD coupling and tau decays

The QCD coupling, $α_s$, 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 $\hat α_s$ and its running is scheme independent. Moreover, scheme variations become completely analogous to renormalization scale variations. We discuss how the coupling $\hat α_s$ 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.

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