Order αs4 QCD corrections to Z and τ decays

Using recently developed methods for the evaluation of five-loop amplitudes in perturbative QCD, corrections of order alpha(4)(s) for the nonsinglet part of the cross section for electron-positron annihilation into hadrons and for the decay rates of the Z boson and the tau lepton into hadrons are evaluated. The new terms lead to a significant stabilization of the perturbative series, to a reduction of the theory uncertainly in the strong coupling constant alpha(s), as extracted from these measurements, and to a small shift of the central value, moving the two central values closer together. The agreement between two values of alpha(s) measured at vastly different energies constitutes a striking test of asymptotic freedom. Combining the results from Z and tau decays we find alpha(s)(M(Z))=0.1198 +/- 0.0015 as one of the most precise and presently only result for the strong coupling constant in order alpha(4)(s).