Measurements of the strong coupling constant and the QCD colour factors using four-jet observables from hadronic Z decays

Abstract.

Data from ${\rm e^+e^-}$ 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 $\alpha_s(M_{\mathrm Z}) = 0.1170 \pm 0.0001 ({\rm stat}) \pm 0.0013 ({\rm sys})$ . In a second measurement the strong coupling constant and the QCD colour factors are determined simultaneously from a fit to the four-jet rate and the four-jet angular correlations, giving $\alpha_s(M_{\rm Z}) = 0.119 \pm 0.006 ({\rm stat}) \pm 0.026 ({\rm sys})$ $C_{\rm A} = 2.93 \pm 0.14 ({\rm stat}) \pm 0.58 ({\rm sys})$ $C_{\rm F} = 1.35 \pm 0.07 ({\rm stat}) \pm 0.26 ({\rm sys})$ in good agreement with the expectation from QCD.