An experimental approach to optimise and test perturbative QCD toO(α _s ² )

Abstract

Production rates of multijet hadronic final states observed ine⁺e⁻ annihilation are compared with recent QCD calculations using renormalisation group improved perturbation theory toO(α _s ² ). The scale parameter\(\Lambda _{\overline {MS} } \) and the renormalisation scaleμ² are adjusted in order to reproduce the observed 2-,3-, and 4-jet event production rates. Small scales ofμ²≈0.002·E _cm ² provide a significantly better description of the overall 4-jet production rates and of 2-and 3-jet rates at small jet pair masses than calculations usingμ²=E _cm ² . The adjusted value of\(\Lambda _{\overline {MS} } \) depends on the choice ofμ². It decreases by a factor of two when going fromμ²=E _cm ² toμ²=0.002·E _cm ² and results in\(\Lambda _{\overline {MS} } = 95 MeV \pm 30 MeV\) MeV±30 MeV for 0.001≦μ²/E _cm ² ≦0.020. The predictions of an Abelian vector theory complete toO(α _s ² ) are not compatible with the observed dynamics of jet production. The experimental evidence for the energy dependence of α _s , obtained from 3-jet event production rates observed in the center of mass energy range between 22 GeV and 56 GeV, does not depend on the detailed choice ofμ².