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We have studied hadronic events from e + e- annihilation data at centre-of-mass energies from 91 to 209 GeV. We present distributions of event shape observables and their moments at each energy and compare with QCD Monte Carlo models. From the event shape distributions we extract the strong coupling $\ensuremath{\alpha_{\mathrm{s}}}$ and test its evolution with energy scale. The results are consistent with the running of $\ensuremath{\alpha_{\mathrm{s}}}$ expected from QCD. Combining all data, the value of $\ensuremath{\alpha_{\mathrm{s}}} \ensuremath{(M_{\mathrm{Z}})}$ is determined to be $ \ensuremath{\alpha_{\mathrm{s}}}\ensuremath{M_{\mathrm{Z}}} = 0.1191\pm0.0005 \mathrm{(stat.)} \pm0.0010\mathrm{(expt.)} \pm0.0011 \mathrm{(hadr.)} \pm0.0044 \mathrm{(theo.)}\,. $ The energy evolution of the moments is also used to determine a value of $\ensuremath{\alpha_{\mathrm{s}}}$ with slightly larger errors: $\ensuremath{\alpha_{\mathrm{s}}}\ensuremath{M_{\mathrm{Z}}}=0.1223\pm 0.0005(\mathrm{stat.})\pm0.0014(\mathrm{expt.})\pm 0.0016(\mathrm{hadr.})^{+0.0054}_{-0.0036}(\mathrm{theo.})$.

european physical journal. c, particles and fields

Measurement of event shape distributions and moments in e + e $^-\rightarrow \mathrm{hadrons}$ at 91-209 GeV and a determination of $\ensuremath{\alpha_{\mathrm{s}}}$