We have studied the structure of hadronic events with a hard, isolated photon in the final state (e + e − → Z → hadrons + γ) in the 3.6 million hadronic events collected with the L3 detector at centre-of-mass energies around 91 GeV. The centre-of-mass energy of the hadronic system is in the range 30 GeV to 86 GeV. Event shape variables have been measured at these reduced centre-of-mass energies and have been compared with the predictions of different QCD Monte Carlo programs. The event shape variables and the energy dependence of their mean values are well reproduced by QCD models. We fit distributions of several global event shape variables to resummed O (α s 2 ) calculations to determine the strong coupling constant α s over a wide range of energies. We find that the strong coupling constant α s decreases with increasing energy, as expected from QCD.
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We have studied hadronic events produced at LEP at a centre-of-mass energy of 161 GeV. We present distributions of event shape variables, jet rates, charged particle momentum spectra and multiplicities. We determine the strong coupling strength to be αs(161 GeV) = 0.101±0.005(stat.)±0.007(syst.), the mean charged particle multiplicity to be 〈nch〉(161 GeV) = 24.46 ± 0.45(stat.) ± 0.44(syst.) and the position of the peak in the ξp = ln(1/xp) distribution to be ξ0(161 GeV) = 4.00 ±0.03(stat.)±0.04(syst.). These results are compared to data taken at lower centre-of-mass energies and to analytic QCD or Monte Carlo predictions. Our measured value of αs(161 GeV) is consistent with other measurements of αs. Within the current statistical and systematic uncertainties, the PYTHIA, HERWIG and ARIADNE QCD Monte Carlo models and analytic calculations are in overall agreement with our measurements. The COJETS QCD Monte Carlo is in general agreement with the data for momentum weighted distributions like Thrust, but predicts a significantly larger charged particle multiplicity than is observed experimentally.
Determination of alpha_s.
Multiplicity and higher moments.
Thrust distribution.
We have studied hadronic events produced at LEP at centre-of-mass energies of 130 and 136 GeV. Distributions of event shape observables, jet rates, momentum spectra and multiplicities are presented and compared to the predictions of several Monte Carlo models and analytic QCD calculations. From fits of event shape and jet rate distributions to\({\mathcal{O}}(\alpha _s^2 ) + NLLA\) QCD calculations, we determineαs(133 GeV)=0.110±0.005(stat.)±0.009(syst.). We measure the mean charged particle multiplicity 〈nch〉=23.40±0.45(stat.) ±0.47(syst.) and the position ζ0 of the peak in the ζp = ln(1/xp) distribution ζ0=3.94±0.05(stat.)±0.11(syst.). These results are compared to lower energy data and to analytic QCD or Monte Carlo predictions for their energy evolution.
Determination of alpha_s.
Multiplicity and high moments.
Tmajor distribution.
We present a study of the structure of hadronic events recorded by the L3 detector at center-of-mass energies of 130 and 136 GeV. The data sample corresponds to an integrated luminosity of 5 pb −1 collected during the high energy run of 1995. The shapes of the event shape distributions and the energy dependence of their mean values are well reproduced by QCD models. From a comparison of the data with resummed O (α s 2 ) QCD calculations, we determine the strong coupling constant to be α s (133 GeV) = 0.107 ± 0.005(exp) ± 0.006(theor).
Mean values of the event shape variables.
Mean charged particle multiplicity.
The value of alpha_s from the fits to the event shape variables : thrust (THRUST), scale heavy jet mass (MH**2/S), total jet broadening (BT)and wide jet broadening (BW). The last value is combined result (COMBINED). The second systematic error is due to uncertainties in the theory.
We describe a cone-based jet finding algorithm (similar to that used in\(\bar p\)p experiments), which we have applied to hadronic events recorded using the OPAL detector at LEP. Comparisons are made between jets defined with the cone algorithm and jets found by the “JADE” and “Durham” jet finders usually used ine+e− experiments. Measured jet rates, as a function of the cone size and as a function of the minimum jet energy, have been compared with O(αs2) calculations, from which two complementary measurements\(\alpha _s \left( {M_{Z^0 } } \right)\) have been made. The results are\(\alpha _s \left( {M_{Z^0 } } \right)\)=0.116±0.008 and\(\alpha _s \left( {M_{Z^0 } } \right)\)=0.119±0.008 respectively, where the errors include both experimental and theoretical uncertainties. Measurements are presented of the energy flow inside jets defined using the cone algorithm, and compared with equivalent data from\(\bar p\)p interactions, reported by the CDF collaboration. We find that the jets ine+e− are significantly narrower than those observed in\(\bar p\)p. The main contribution to this effect appears to arise from differences between quark- and gluon-induced jets.
Measured 2 jet production rate as a function of EPSILON, the minimum energy of a jet for a fixed cone radius R = 0.7 radians.
Measured 2 jet production rate as a function of R, the jet cone radius, for a fixed value of the minimum jet energy, EPSILON, of 7 GeV.
Measured 3 jet production rate as a function of EPSILON, the minimum energy of a jet for a fixed cone radius R = 0.7 radians.
This experiment was performed with the SLD detector at the Stanford Linear Accelerator Center. Only charged tracks measured in the central drift chamber were used for the measurement of the jet production rates. The value of the strong coupling $\alpha_s (M_{Z^0})$ is determined from the production rates of jets in hadronic $Z^0$ decays in $e^+e^-$ annihilations. The relative jet rates are obtained using the JADE-type algorithms. The results are compared with the jet rates obtained from a new jet algorithm proposed by N. Brown et al. called the "Durham" algorithm. The data can be well described by $\mathcal{O}(\alpha^2_s)$ QCD calculations and by QCD shower model calculations. A fit of the theoretical predictions to the data taken with the SLD yields a value$\alpha_s(M_{Z^0})$ = $0.120 \pm 0.002(stat.) \pm 0.003(exp.)^{+0.011}_{-0.009}(theor.)$ The error is dominated by the theoretical uncertainties. The measurement is compared with results from other experiments and it is shown that the value obtained for $\alpha_s$ agrees well with these results and furthermore supports the evidence for the running of the strong coupling, consistent with the non-Abelian nature of QCD. The Stanford Linear Collider (SLC) can deliver partially longitudinally polarized electrons to the interaction point. Jet production rates and values for a, are calculated both for right-handed and left-handed initial state electrons. All results are consistent with the unpolarized result, as predicted by the Standard Model.
Jet production rates using the JADE recombination scheme.
Jet production rates using the DURHAM recombination scheme.
Jet production rates using the E recombination scheme.
The value of the strong coupling constant,$$\alpha _s (M_{Z^0 } )$$, is determined from a study of 15 d
Differential jet mass distribution for the heavier jet using method T. The data are corrected for the finite acceptance and resolution of the detector and for initial state photon radiation.
Differential jet mass distribution for the jet mass difference using methodT. The data are corrected for the finite acceptance and resolution of the detec tor and for initial state photon radiation.
Differential jet mass distribution for the heavier jet using method M. The data are corrected for the finite acceptance and resolution of the detector and for initial state photon radiation.
Distributions of event shape variables obtained from 120600 hadronicZ decays measured with the DELPHI detector are compared to the predictions of QCD based event generators. Values of the strong coupling constant αs are derived as a function of the renormalization scale from a quantitative analysis of eight hadronic distributions. The final result, αs(MZ), is based on second order perturbation theory and uses two hadronization corrections, one computed with a parton shower model and the other with a QCD matrix element model.
Experimental differential Thrust distributions.
Experimental differential Oblateness distributions.
Experimental differential C-parameter distributions.
An analysis of global event-shape variables has been carried out for the reaction e + e − →Z 0 →hadrons to measure the strong coupling constant α s . This study is based on 52 720 hadronic events obtained in 1989/90 with the ALEPH detector at the LEP collider at energies near the peak of the Z-resonance. In order to determine α s , second order QCD predictions modified by effects of perturbative higher orders and hadronization were fitted to the experimental distributions of event-shape variables. From a detailed analysis of the theoretical uncertainties we find that this approach is best justified for the differential two-jet rate, from which we obtain α s ( M Z 2 ) = 0.121 ± 0.002(stat.)±0.003(sys.)±0.007(theor.) using a renormalization scale ω = 1 2 M Z . The dependence of α s ( M Z 2 ) on ω is parameterized. For scales m b <ω< M Z the result varies by −0.012 +0.007 .
The second DSYS error is the theoretical error.
The error includes the experimental uncertainties (±0.003), uncertainties of hadronisation corrections and of the degree of parton virtualities to which the data are corrected, as well as the uncertainty of choosing the renormalisation scale.
Jet production rates using the E0 recombination scheme.
Jet production rates using the E recombination scheme.
Jet production rates using the p0 recombination scheme.