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.
Infrared and collinear safe event shape distributions and their mean values are determined using the data taken at five different centre of mass energies above M Z with the DELPHI detector at LEP. From the event shapes, the strong coupling α s is extracted in O ( α s 2 ), NLLA and a combined scheme using hadronisation corrections evaluated with fragmentation model generators as well as using an analytical power ansatz. Comparing these measurements to those obtained at M Z , the energy dependence (running) of α s is accessible. The logarithmic energy slope of the inverse strong coupling is measured to be d α −1 s d log (E cm ) =1.39±0.34( stat )±0.17( syst ) , in good agreement with the QCD expectation of 1.27.
Moments of the (1-THRUST) distributions at cm energies 133, 161, 172 and 183 GeV.
Moments of the Thrust Major distributions at cm energies 133, 161, 172 and 183 GeV.
Moments of the Thrust Minor distributions at cm energies 133, 161, 172 and 183 GeV.
Mean values and differential distributions of event-shape variables have been studied in neutral current deep inelastic scattering using an integrated {luminosity} of 82.2 pb$^{-1}$ collected with the ZEUS detector at HERA. The kinematic range was $80 < Q^2 < 20 480\gev^2$ and $0.0024 < x < 0.6$, where $Q^2$ is the virtuality of the exchanged boson and $x$ is the Bjorken variable. The data are compared with a model based on a combination of next-to-leading-order QCD calculations with next-to-leading-logarithm corrections and the Dokshitzer-Webber non-perturbative power corrections. The power-correction method provides a reasonable description of the data for all event-shape variables studied. Nevertheless, the lack of consistency of the determination of $\alpha_s$ and of the non-perturbative parameter of the model, $\albar$, suggests the importance of higher-order processes that are not yet included in the model.
Mean value of the event shape variable 1-THRUST(C=T).
Mean value of the event shape variable B(C=T).
Mean value of the event shape variable RHO**2.
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