Testing QCD with Hypothetical Tau Leptons

We construct new tests of perturbative QCD by considering a hypothetical τ lepton of arbitrary mass, which decays hadronically through the electromagnetic current. We can explicitly compute its hadronic width ratio directly as an integral over the e+e- annihilation cross section ratio, Re+e-. Furthermore, we can design a set of commensurate scale relations and perturbative QCD tests by varying the weight function away from the form associated with the V-A decay of the physical τ. This method allows the wide range of the Re+e- data to be used as a probe of perturbative QCD