Determination of $alpha_s$ using OPAL hadronic event shapes at $\sqrt{s}=91$ - 209 GeV and resummed NNLO calculations

Hadronic event shape distributions from e(+)e(-) 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(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 re-summed next-to-leading-log-approximation terms (NNLO+NLLA). The combined NNLO result from all variables and centre-of-mass energies is alpha(S)(m(Z0)) = 0.1201 +/- 0.0008 ( stat.) +/- 0.0013(exp.) +/- 0.0010(had.) +/- 0.0024(theo.) while the combined NNLO + NLLA result is alpha(S)(m(Z0)) = 0.1189 +/- 0.0008( stat.) +/- 0.0016(exp.) +/- 0.0010(had.) +/- 0.0036(theo.) 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(S) agrees with the QCD prediction of asymptotic freedomand excludes the absence of running.