Tests of quantum chromo dynamics at e⁺e^-colliders

The current status of tests of the theory of strong interactions, quantum chromo dynamics (QCD), with data from hadron production in e⁺e^-annihilation experiments is reviewed. The LEP experiments ALEPH, DELPHI, L3 and OPAL have published many analyses with data recorded on the Z⁰resonance atand above up to. There are also results from SLD atand from reanalysis of data recorded by the JADE experiment at. The results of studies of jet and event shape observables, particle production and quark gluon jet differences are compared with predictions by perturbative QCD calculations. Determinations of the strong coupling constantfrom jet and event shape observables, scaling violation and fragmentation functions (FFs), inclusive observables from Z⁰decays, hadronic τ decays and hadron production in low-energy e⁺e^-annihilation are discussed. Updates of the measurements are performed where new data or improved calculations have become available. The best value ofis obtained from an average of measurements using inclusive observables calculated in NNLO QCD:where the error is dominated by theoretical systematic uncertainties. The other measurements ofare in good agreement with this value. Finally, investigations of the gauge structure of QCD are summarized and the best values for the colour factors are determined:with errors dominated by systematic uncertainties and in good agreement with the expectation from QCD with the SU(3) gauge symmetry.