Determination of $\alpha_s$ in First and Second Order {QCD} From $e^+ e^-$ Annihilation Into Hadrons

Multihadron events produced bye + e − annihilation at a c.m. energy of 34.6 GeV have been used to determine α s . The predictions of 1 st and 2nd order QCD models with independent jet and string fragmentation have been compared to a large variety of kinematic variables such as event shapes, transverse momentum spectra, jet masses, 3-cluster thrust and the asymmetry of energy-energy correlations. The value of α s has been found to depend on the variables used, on the fragmentation model and on the treatment of soft gluons in the 2nd order QCD calculation. Within the models considered α s has been found in complete 2nd order QCD to lie between 0.12 and 0.23.