Testing QCD with hypothetical tau leptons

Abstract

We construct new phenomenological tests of perturbative QCD by considering a hypothetical au lepton of arbitrary mass which decays hadronically through the electromagnetic current. Its adronic 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 τ . 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. [S0556-2821(99)05713-6].