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Testing QCD with Hypothetical Tau Leptons


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.

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