Deep-inelastic ep scattering data taken with the H1 detector at HERA and corresponding to an integrated luminosity of 106 pb^{-1} are used to study the differential distributions of event shape variables. These include thrust, jet broadening, jet mass and the C-parameter. The four-momentum transfer Q is taken to be the relevant energy scale and ranges between 14 GeV and 200 GeV. The event shape distributions are compared with perturbative QCD predictions, which include resummed contributions and analytical power law corrections, the latter accounting for non-perturbative hadronisation effects. The data clearly exhibit the running of the strong coupling alpha_s(Q) and are consistent with a universal power correction parameter alpha_0 for all event shape variables. A combined QCD fit using all event shape variables yields alpha_s(mZ) = 0.1198 \pm 0.0013 ^{+0.0056}_{-0.0043} and alpha_0 = 0.476 \pm 0.008 ^{+0.018} _{-0.059}.
Normalised distribution of (1-THRUST) where THRUST is w.r.t the axis which maximises the sum of the longitudinal momenta in the current hemisphere, for Q = 14.0 to 16.0 GeV and X = 0.00841 .
Normalised distribution of (1-THRUST) where THRUST is w.r.t the axis which maximises the sum of the longitudinal momenta in the current hemisphere, for Q = 16.0 to 20.0 GeV and X = 0.01180 .
Normalised distribution of (1-THRUST) where THRUST is w.r.t the axis which maximises the sum of the longitudinal momenta in the current hemisphere, for Q = 20.0 to 30.0 GeV and X = 0.02090 .
We have studied hadronic events from e+e- annihilation data at centre-of-mass energies from 91 to 209 GeV. We present distributions of event shape observables and their moments at each energy and compare with QCD Monte Carlo models. From the event shape distributions we extract the strong coupling alpha_s and test its evolution with energy scale. The results are consistent with the running of alpha_s expected from QCD. Combining all data, the value of alpha_s(M_Z) is determined to be alpha_s(M_Z) = 0.1191 +- 0.0005 (stat.) +- 0.0010 (expt.) +- 0.0011 (hadr.) +- 0.0044 (theo.). The energy evolution of the moments is also used to determine a value of alpha_s with slightly larger errors: alpha_s(M_Z) = 0.1223 +- 0.0005 (stat.) +- 0.0014 (expt.) +- 0.0016 (hadr.) +0.0054 -0.0036 (theo.).
Measured normalized differential distribution for 1-THRUST.
Measured normalized differential distribution for HEAVY-JET-MASS.
Measured normalized differential distribution for C-PARAMETER.
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.
Inclusive event-shape variables have been measured in the current region of the Breit frame for neutral current deep inelastic ep scattering using an integrated luminosity of 45.0 pb^-1 collected with the ZEUS detector at HERA. The variables studied included thrust, jet broadening and invariant jet mass. The kinematic range covered was 10 < Q^2 < 20,480 GeV^2 and 6.10^-4 < x < 0.6, where Q^2 is the virtuality of the exchanged boson and x is the Bjorken variable. The Q dependence of the shape variables has been used in conjunction with NLO perturbative calculations and the Dokshitzer-Webber non-perturbative corrections (`power corrections') to investigate the validity of this approach.
Mean value of the event shape variables 1-THRUST(C=T) in different Q**2 and X bins.
Mean value of the event shape variables B(C=T) in different Q**2 and X bins.
Mean value of the event shape variables RHO**2 in different Q**2 and X bins.
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.
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