We construct new tests of perturbative QCD by considering a hypothetical tau
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, R_{e^+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 tau. This method allows the wide
range of the R_{e^+e^-} data to be used as a probe of perturbative QCD.Comment: 4 pages, 4 figure
