Infrared and collinear safe event shape distributions and their mean values are determined in e+e- collisions at centre-of-mass energies between 45 and 202 GeV. A phenomenological analysis based on power correction models including hadron mass effects for both differential distributions and mean values is presented. Using power corrections, alpha_s is extracted from the mean values and shapes. In an alternative approach, renormalisation group invariance (RGI) is used as an explicit constraint, leading to a consistent description of mean values without the need for sizeable power corrections. The QCD beta-function is precisely measured using this approach. From the DELPHI data on Thrust, including data from low energy experiments, one finds beta_0 = 7.86 +/- 0.32 for the one loop coefficient of the beta-function or, assuming QCD, n_f = 4.75 +/- 0.44 for the number of active flavours. These values agree well with the QCD expectation of beta_0=7.67 and n_f=5. A direct measurement of the full logarithmic energy slope excludes light gluinos with a mass below 5 GeV.
1-THRUST distribution.
THRUST-MAJOR distribution.
THRUST-MINOR distribution.
The jet character of the hadronic final states produced ine+e− annihilations is studied in terms of jet measures such as thrust, sphericity, jet opening angle and jet masses, in the energy range 7.7 to 31.6 GeV. All distributions and averages have been corrected for detector effects and initial state radiation. The energy dependence of the averages of these jet quantities is used to estimate the contributions due to perturbative QCD and fragmentation effects. Correlations between the jet measures and the multiplicity of charged hadrons are also presented.
DIFFERENTIAL THRUST DISTRIBUTIONS WHERE THRUST IS MAX(SUM(ABS(PLONG))/SUM(ABS(P))).
MEAN THRUST VALUES AS A FUNCTION OF CM ENERGY.
DIFFERENTIAL SPERICITY DISTRIBUTIONS WHERE SPHERICITY IS 3/2*MIN(SUM(PT**2)/SUM(ABS(P))).
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