Determination of alpha sub(S) using OPAL hadronic event shapes at $\sqrt{s} = 91\mbox{--}209~\mathrm{GeV}$ and resummed NNLO calculations

Hadronic event shape distributions from e super(+)e super(-) annihilation measured by the OPAL experiment at centre-of-mass energies between 91 GeV and 209 GeV are used to determine the strong coupling alpha sub(S). The results are based on QCD predictions complete to the next-to-next-to-leading order (NNLO), and on NNLO calculations matched to the resummed next-to-leading-log-approximation terms (NNLO+NLLA). The combined NNLO result from all variables and centre-of-mass energies is while the combined NNLO+NLLA result is The completeness of the NNLO and NNLO+NLLA results with respect to missing higher order contributions, studied by varying the renormalization scale, is improved compared to previous results based on NLO or NLO+NLLA predictions only. The observed energy dependence of alpha sub(S) agrees with the QCD prediction of asymptotic freedom and excludes the absence of running.