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 M Z with the DELPHI detector at LEP. From the event shapes, the strong coupling α s is extracted in O ( α s 2), 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 M Z, the energy dependence (running) of α s is accessible. The logarithmic energy slope of the inverse strong coupling is measured to be d α −1 s d log(E cm ) =1.39±0.34( stat)±0.17( syst) , in good agreement with the QCD expectation of 1.27.