Abstract
The data collected with Delphi during the Lep1 period is used to perform a simultaneous fit to the strong coupling constant α s in 2 nd order perturbation theory and to the renormalisation scale χ μ . The results are compared to α s fits in 2 nd order perturbation theory with fixed scale χ μ and to other theoretically motivated scale setting methods. To determine the energy dependence of α s , event shape distributions and their mean values are measured for √ s = 48 GeV to 189 GeV. The strong coupling α s is extractd in O ( α s 2), Next to Leading Log Approximation (NLLA) and in a combined scheme using hadronisation corrections-evaluated with fragmentation model generators, and an analytical power ansatz.
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