Scheme variations of the QCD coupling

Abstract

The Quantum Chromodynamics (QCD) coupling $\alpha_s$ is a central parameter in the Standard Model of particle physics. However, it depends on theoretical conventions related to renormalisation and hence is not an observable quantity. In order to capture this dependence in a transparent way, a novel definition of the QCD coupling, denoted by $\hat a$, is introduced, whose running is explicitly renormalisation scheme invariant. The remaining renormalisation scheme dependence is related to transformations of the QCD scale $\Lambda$, and can be parametrised by a single parameter $C$. Hence, we call $\hat a$ the $C$-scheme coupling. The dependence on $C$ can be exploited to study and improve perturbative predictions of physical observables. This is demonstrated for the QCD Adler function and hadronic decays of the $\tau$ lepton.