Studies of QCD at ${rm e}^ + {rm e}^-$ centre-of-mass energies between 91 and 209 GeV

The hadronic final states observed with the ALEPH detector at LEP in annihilation are analysed using 730 pb^-1 of data collected between 91 and 209 GeV in the framework of QCD. In particular event-shape variables and inclusive charged particle spectra are measured. The energy evolution of quantities derived from these measurements is compared to analytic QCD predictions. The mean charged particle multiplicity, the charged particle momentum spectrum and its peak position are compared to predictions of the modified-leading-logarithmic approximation. The strong coupling constant is determined from a fit of the QCD prediction to distributions of six event-shape variables at eight centre-of-mass energies. A study of non-perturbative power law corrections is presented.Received: 18 May 2004, Published online: 23 June 2004