Energy dependence of event shapes and of αs at LEP 2

Infrared and collinear safe event shape distributions and their mean values are determined using the data taken at five different centre of mass energies above MZ with the DELPHI detector at LEP. From the event shapes, the strong coupling αs is extracted in O(αs2), NLLA and a combined scheme using hadronisation corrections evaluated with fragmentation model generators as well as using an analytical power ansatz. Comparing these measurements to those obtained at MZ, the energy dependence (running) of αs is accessible. The logarithmic energy slope of the inverse strong coupling is measured to bed α−1sd log(Ecm)=1.39±0.34(stat)±0.17(syst) ,in good agreement with the QCD expectation of 1.27.