Complete QCD Corrections to Hadronic $Z$--Decays in Order $\alpha_s^4$

TL;DR

This paper presents the first complete order α_s^4 calculation of the Z-boson hadronic decay rate, improving precision and stability of theoretical predictions in quantum chromodynamics.

Contribution

It provides the first complete α_s^4 order prediction for Z-boson hadronic decay rates, including axial singlet contributions in the heavy top quark limit.

Findings

Significant stabilization of the perturbative series.

Reduced theoretical uncertainty in α_s extraction.

Small shift in the central value of α_s.

Abstract

Corrections of order $\alpha_s^4$ for the axial singlet contributions for the decay rates of the $Z$-boson into hadrons are evaluated in the limit of the heavy top quark mass. Combined with recently finished ${\cal O}(\alpha_s^4)$ calculations of the non-signlet corrections, the new results directly lead us to the first {\em complete} ${\cal O}(\alpha_s^4)$ prediction for the total hadronic decay rate of the Z-boson. The new ${\cal O}(\alpha_s^4)$ term in Z-decay rate lead to a significant stabilization of the perturbative series, to a reduction of the theory uncertainty in the strong coupling constant $\alpha_s$, as extracted from these measurements, and to a small shift of the central value.