Order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>α</mml:mi><mml:mi>s</mml:mi><mml:mn>4</mml:mn></mml:msubsup></mml:math>QCD Corrections to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math>Decays

Alphas(MZ)=0.1198+/-0.0015 as one of the most precise and presently only result for the strong coupling constant in order alphas4, and a striking test of asymptotic freedom.

Abstract

Using recently developed methods for the evaluation of five-loop amplitudes in perturbative QCD, corrections of order alphas4 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 alphas, 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 alphas measured at vastly different energies constitutes a striking test of asymptotic freedom. Combining the results from Z and tau decays we find alphas(MZ)=0.1198+/-0.0015 as one of the most precise and presently only result for the strong coupling constant in order alphas4.