Renormalization-scale-invariant PQCD predictions forRe+e−and the Bjorken sum rule at next-to-leading order

Abstract

We discuss the application of the physical QCD effective charge ${\ensuremath{\alpha}}_{V},$ defined via the heavy-quark potential, in perturbative calculations at next-to-leading order. When coupled with the Brodsky-Lepage-Mackenzie prescription for fixing the renormalization scales, the resulting series are automatically and naturally scale and scheme independent, and represent unambiguous predictions of perturbative QCD. We consider in detail such commensurate scale relations for the ${e}^{+}{e}^{\ensuremath{-}}$ annihilation ratio ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ and the Bjorken sum rule. In both cases the improved predictions are in excellent agreement with experiment.