Testing QCD with hypothetical tau leptons

We construct new phenomenological tests of perturbative QCD by considering a hypothetical $\tau$ lepton of arbitrary mass which decays hadronically through the electromagnetic current. Its hadronic branching ratio can be computed directly as an integral over the $e^{+}{e}^{-}$ annihilation cross section ratio, $R_{e^{+}{e}^{-}}.$ More generally, we can design a set of commensurate scale relations which test the applicability and self-consistency of leading twist QCD predictions by varying the weight function away from the form associated with the $V-A$ decay of the physical $\tau .$ This method allows the wide range of $R_{e^{+}{e}^{-}}$ data (or other similar observables which define an effective charge) to be used as renormalization scheme and scale invariant probes of QCD.