QCD predictions for the decay of theτlepton

Abstract

The semileptonic decay rate of a heavy lepton is shown to be rigorously calculable by use of perturbative QCD. Even the τ lepton is heavy enough for the perturbative approximation to be accurate. The prediction for the ratio R=Γ(τ→${\mathit{v}}_{\mathrm{\tau }}$+hadrons)/Γ(τ→${\mathit{v}}_{\mathrm{\tau }}$+${\mathit{e}}^{\mathrm{-}}$+v${\mathrm{¯}}_{\mathit{e}}$) is 3.29, with an uncertainty of about 1% due to the uncertainty in the Λ parameter of QCD. Nonperturbative corrections to this prediction are estimated to be on the order of 1%. More importantly, these corrections are shown to be negative because of a fortuitous cancellation of the leading contribution from the gluon condensate. The resulting prediction is significantly smaller than the present experimental result R=3.65±0.13.