Hadronic Z- and tau-Decays in Order alpha_s^4

TL;DR

This paper computes five-loop order alpha_s^4 corrections in perturbative QCD for hadronic Z- and tau-decays, significantly improving the precision of the strong coupling constant alpha_s and testing asymptotic freedom.

Contribution

It presents the first evaluation of alpha_s^4 order corrections for key hadronic decay processes using advanced five-loop amplitude methods, enhancing theoretical precision.

Findings

Reduced theoretical uncertainty in alpha_s extraction

Shifted central values of alpha_s closer at different energies

Achieved one of the most precise alpha_s(M_Z) measurements

Abstract

Using recently developed methods for the evaluation of five-loop amplitudes in perturbative QCD, corrections of order alpha_s^4 for the cross section of 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 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 \pm 0.0015 as one of the most precise and presently only result for the strong coupling constant in order alpha_s^4.