Precision physics with QCD

Understand

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 $\alpha_s(M_Z^2)= 0.1197 \pm 0.0015$.