The relative production ratio of 3-jet events to the total number of hadronic events was studied in e + e − annihilations at centre-of-mass energies between 54 and 61.4 GeV. The QCD scale parameter has been determined to be Λ MS =254 −47 +55 ±56 MeV on the basis of a QCD cascade with the next-to-leading logarithmic approximation.
Data are uncorrected for initial radiation, detector effects, and quark hadronization.
LAMBDA-MSBAR determined from the 3-jet ratio.
We have measured the total e + e − hadronic annihilation cross section at the center of mass energies between 50.0 GeV and 61.4 GeV with the TOPAZ detector at TRISTAN. The full electroweak radiative corrections (up to O(α 3 )) were applied to the data which were analysed together with the published data from PEP and PETRA. We then determined the standard model parameters, M z (the mass of the Z), sin w 2 θ (the Weinberg angle) and Λ MS (the QCD scale parameter) by comparing the experimental data with the prediction of the standard model. The best fit values are M z = 89.2 −1.8 +2.1 GeV/c 2 , sin 2 θ w = 0.233 −0.025 +0.035 and Λ MS = 0.327 −0.206 +0.275 GeV. A constraint is obtained on the heavy top quark mass through the radiative corrections if we take the SLC value of M z (91.1 GeV / c 2 ).
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