Measurements of the Strong Coupling Constant and the QCD Colour Factors using Four-jet Observables from Hadronic Z Decays

Data from e+e- annihilation into hadrons, taken with the ALEPH detector at the Z resonance, are analyzed. The four-jet rate is studied as a function of the resolution parameter and compared to next-to-leading order calculations combined with resummation of large logarithms. Angular correlations in four-jet events are measured and compared to next-to-leading order QCD predictions. With these observables two different measurements are performed. In a first analysis the strong coupling constant is measured from the four-jet rate yielding alpha_s(M_ Z}) = 0.1170 \pm 0.0001(stat) \pm 0.0014(sys) In a second measurement the strong coupling constant and the \textsc{QCD} colour factors are determined simultaneously from a fit to the four-jet rate and the four-jet angular correlations, giving alpha_s(M_ Z) = 0.119 \pm 0.006(stat) \pm 0.026 (sys) C_A = 2.93 \pm 0.14(stat) \pm 0.58 (sys) C_F} = 1.35 \pm 0.07 (stat) \pm 0.26 (sys) in good agreement with the expectation from QCD