Large-order perturbation theory for the electromagnetic current-current correlation function

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 α[over ^]_{s}, whose running is explicitly renormalization scheme invariant. The scheme dependence of the new coupling α[over ^]_{s} is parametrized 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.