Multijet-Produktion in der $e^+e^--$Annihilation von $\sqrt{s}=$89 GeV bis 207 GeV: Messung der starken Kopplung $\alpha_s$ aus der Vierjetrate

Hadronic events from the data collected with the DELPHI detector at LEP within an energy range from 89 GeV to 207 GeV are selected and their jet rates are determined. The measurement of jet rates give no indication for an excess of multi jet events at high energies. The four jet rate is compared to next to leading order calculations. Studies on the influence of the renormalisation scale μ are performed confirming previous DELPHI results on optimised scales. Applying scale optimisation methods allows a precise measurement of the strong coupling αs from LEP1 data. The final result is obtained by the CAMBRIDGE algorithm: = 0:1175 ± 0:0010(exp:) ± 0:0017(hadr:) ± 0:0007(scale) . The comparison of αs as measured at the Z and at higher energies gives access to the energy dependence (running) of the strong coupling. The logarithmic energy slope, again obtained from Cambridge, is measured to be = 1:14 ± 0:25(stat:) ± 0:25(sys:) , while the QCD prediction for this quantity is 1.28. The results in are in good agreement with previous, statistically uncorrelated measurements based on three jet final states.