Testing QCD with Hypothetical Tau Leptons

Abstract

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{sup +}e{sup -} annihilation cross section ratio, R{sub e{sup +}e{sup -}}. 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{sub e{sup +}e{sup -}} data to be used as a probe of perturbative QCD.