Scheme variations of the QCD coupling and hadronic $τ$ decays

The Quantum Chromodynamics (QCD) coupling, $α_s$, is not a physical observable of the theory since it depends on conventions related to the renormalization procedure. We introduce a definition of the QCD coupling, denoted by $\hatα_s$, whose running is explicitly renormalization scheme invariant. The scheme dependence of the new coupling $\hatα_s$ is parameterized by a single parameter $C$, related to transformations of the QCD scale $Λ$. It is demonstrated that appropriate choices of $C$ can lead to substantial improvements in the perturbative prediction of physical observables. As phenomenological applications, we study $e^+e^-$ scattering and decays of the $τ$ lepton into hadrons, both being governed by the QCD Adler function.

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