New Tests of Perturbative QCD Inspired by Hypothetical Tau Leptons

Inspired by the relation between the hadronic decay of the tau lepton and the electron-positron annihilation into hadrons, we derive new tests of perturbative QCD. We design a set of commensurate scale relations to test the self-consistency of leading-twist QCD predictions for any observable which defines an effective charge. This method provides renormalization scheme and scale invariant probes of QCD which can be applied over wide data ranges.