Measurement ofαsfrom energy-energy correlations at theZ0resonance

We determine the strong coupling ${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$ from a comprehensive study of energy-energy correlations (EEC's) and their asymmetry (AEEC's) in hadronic decays of ${\mathit{Z}}^{0}$ bosons collected by the SLD experiment at SLAC. The data are compared with all four available predictions of QCD calculated up to O(${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}^{2}$) in perturbation theory, and also with a resummed calculation matched to all four of these calculations. We find large discrepancies between ${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$ values extracted from the different O(${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}^{2}$) calculations. We also find a large renormalization scale ambiguity in ${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$ determined from the EEC's using the O(${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}^{2}$) calculations; this ambiguity is reduced in the case of the AEEC's and is very small when the matched calculations are used. Averaging over all calculations, and over the EEC and AEEC results, we obtain ${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$(${\mathit{M}}_{\mathit{Z}}^{2}$)=0.${124}_{\mathrm{\ensuremath{-}}0.004}^{+0.003}$ (expt.) \ifmmode\pm\else\textpm\fi{}0.009 (theory).