Experimental Tests of Asymptotic Freedom

Abstract

Measurements which probe the energy dependence of $\alpha_s$, the coupling strength of the strong interaction, are reviewed. Jet counting in $e^+ e^-$ annihilation, combining results obtained in the centre of mass energy range from 22 to 133 GeV, provides direct evidence for an asymptotically free coupling, without the need to determine explicit values of $\alpha_s$. Recent results from jet production in $e p$ and in $p \overline{p}$ collisions, obtained in single experiments spanning large ranges of momentum transfer, $Q^2$, are in good agreement with the running of $\alpha_s$ as predicted by QCD. Mass spectra of hadronic decays of $\tau$-leptons are analysed to probe the running $\alpha_s$ in the very low energy domain, $0.7 GeV^2 < Q^2 < M_\tau^2$. An update of the world summary of measurements of $\alpha_s(Q^2)$ consistently proves the energy dependence of $\alpha_s$ and results in a combined average of $\alpha_s(M_Z) = 0.118 \pm 0.006$.