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

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 alpha_s and test its evolution with energy scale. The results are consistent with the running of alpha_s expected from QCD. Combining all data, the value of alpha_s (M_z) is determined to be alpha_s(Mz)=0.1191+-0.0005(stat.)+-0.0010 (expt.)+-0.0011(hadr.)+-0.0044(theo.) The energy evolution of the moments is also used to determine a value of alpha_ with slightly larger errors: alpha_s(Mz)=0.1223+-0.0005(stat.) +-0.0014(expt.) +-0.0016(hadr.) +0.0054 -0.0036 (theo). 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 alpha_s and test its evolution with energy scale. The results are consistent with the running of alpha_s expected from QCD. Combining all data, the value of alpha_s(M_Z) is determined to be alpha_s(M_Z) = 0.1191 +- 0.0005 (stat.) +- 0.0010 (expt.) +- 0.0011 (hadr.) +- 0.0044 (theo.). The energy evolution of the moments is also used to determine a value of alpha_s with slightly larger errors: alpha_s(M_Z) = 0.1223 +- 0.0005 (stat.) +- 0.0014 (expt.) +- 0.0016 (hadr.) +0.0054 -0.0036 (theo.).