Abstract
Inspired by the relation between the hadronic decay of the {tau} lepton and the e{sup +}e{sup {minus}} 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.
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