Precision physics with QCD

TL;DR

This paper reviews the four-loop determination of the strong coupling constant from inclusive observables, emphasizing low-energy measurements from tau decay and confirming the consistency of QCD predictions across different energy scales.

Contribution

It provides a comprehensive analysis of the strong coupling from tau decay data, including recent results that confirm the suppression of non-perturbative effects and validate asymptotic freedom.

Findings

Determined alpha_s(m_tau^2)= 0.328 ± 0.013

Derived alpha_s(M_Z^2)= 0.1197 ± 0.0015

Confirmed consistency with measurements at the Z peak

Abstract

The four-loop determination of the strong coupling from fully inclusive observables is reviewed. Special attention is given to the low-energy measurement extracted from the hadronic $\tau$ decay width. A recent exhaustive analysis of the ALEPH data, exploring several complementary methodologies with very different sensitivities to inverse power corrections and duality violations, confirms the strong suppression of non-perturbative contributions to $R_\tau$. It gives the value $\alpha_s(m_\tau^2)= 0.328 \pm 0.013$, which implies $\alpha_s(M_Z^2)= 0.1197 \pm 0.0015$. The excellent agreement with the direct measurement at the $Z$ peak, $\alpha_s(M_Z^2)= 0.1196 \pm 0.0030$, provides a beautiful test of asymptotic freedom. Together with the most recent lattice average from FLAG and the NNLO determinations from $e^+e^-$, PDFs and collider data quoted by the PDG, these two inclusive determinations imply a world average value $\alpha_s(M_Z^2)= 0.1180 \pm 0.0010$.