Studies of event shape observables with the OPAL detector at LEP

In quark-antiquark pair production at LEP, many features of the hadronic final state can be predicted by QCD. Using data collected by the OPAL experiment, we present the statistical distributions of fourteen "event shape observables," which describe the inclusive kinematic properties of events producing three or more jets. For six of these observables, we compare the measured distributions with those calculated in perturbative QCD. By optimising the agreement between theory and data, we measure the strong coupling $\alpha_s$ at a range of energy scales. We also test the predictions of three Monte Carlo event generators, for all fourteen observables. Over the years since the LEP experiments began operating, many similar analyses have been published, and have contributed to the world average measurements of $\alpha_s$. However, several improvements have now been made, both in the theoretical calculations and in the experimental analysis techniques. We therefore present a complete reanalysis of the OPAL data, over the full range of LEP collision energies. Particular attention is given to the estimation of uncertainties, including the large contribution due to uncalculated higher-order terms of the theory predictions. In collaboration with the LEP QCD Working Group, we have combined the $\alpha_s$ measurements obtained from event shape observables by all four experiments. Detailed investigations were undertaken to ensure consistent implementation of the theoretical predictions and uncertainty estimates, and to take account of correlations between measurements.