An updated analysis using about 1.5 million events recorded at $\sqrt{s} = M_Z$ with the DELPHI detector in 1994 is presented. Eighteen infrared and collinear safe event shape observables are measured as a function of the polar angle of the thrust axis. The data are compared to theoretical calculations in ${\cal O} (\alpha_s^2)$ including the event orientation. A combined fit of $\alpha_s$ and of the renormalization scale $x_{\mu}$ in $\cal O(\alpha_s^2$) yields an excellent description of the high statistics data. The weighted average from 18 observables including quark mass effects and correlations is $\alpha_s(M_Z^2) = 0.1174 \pm 0.0026$. The final result, derived from the jet cone energy fraction, the observable with the smallest theoretical and experimental uncertainty, is $\alpha_s(M_Z^2) = 0.1180 \pm 0.0006 (exp.) \pm 0.0013 (hadr.) \pm 0.0008 (scale) \pm 0.0007 (mass)$. Further studies include an $\alpha_s$ determination using theoretical predictions in the next-to-leading log approximation (NLLA), matched NLLA and $\cal O(\alpha_s^2$) predictions as well as theoretically motivated optimized scale setting methods. The influence of higher order contributions was also investigated by using the method of Pad\'{e} approximants. Average $\alpha_s$ values derived from the different approaches are in good agreement.
The weighted value of ALPHA-S from all the measured observables using experimentally optimized renormalization scale values and corrected for the b-mass toleading order.
The value of ALPHA-S derived from the JCEF and corrected for heavy quark mass effects. The quoted errors are respectively due to experimental error, hadronization, renormalization scale and heavy quark mass correction uncertainties.
Energy Energy Correlation EEC.
We report on an improved measurement of the value of the strong coupling constant σ s at the Z 0 peak, using the asymmetry of the energy-energy correlation function. The analysis, based on second-order perturbation theory and a data sample of about 145000 multihadronic Z 0 decays, yields α s ( M z 0 = 0.118±0.001(stat.)±0.003(exp.syst.) −0.004 +0.0009 (theor. syst.), where the theoretical systematic error accounts for uncertainties due to hadronization, the choice of the renormalization scale and unknown higher-order terms. We adjust the parameters of a second-order matrix element Monte Carlo followed by string hadronization to best describe the energy correlation and other hadronic Z 0 decay data. The α s result obtained from this second-order Monte Carlo is found to be unreliable if values of the renormalization scale smaller than about 0.15 E cm are used in the generator.
Value of LAMBDA(MSBAR) and ALPHA_S.. The first systematic error is experimental, the second is from theory.
The EEC and its asymmetry at the hadron level, unfolded for initial-state radiation and for detector acceptance and resolution. Errors include full statistical and systematic uncertainties.
We present a study of energy-energy correlations based on 83 000 hadronic Z 0 decays. From this data we determine the strong coupling constant α s to second order QCD: α s (91.2 GeV)=0.121±0.004(exp.)±0.002(hadr.) −0.006 +0.009 (scale)±0.006(theor.) from the energy-energy correlation and α s (91.2 GeV)=0.115±0.004(exp.) −0.004 +0.007 (hadr.) −0.000 +0.002 (scale) −0.005 +0.003 (theor.) from its asymmetry using a renormalization scale μ 1 =0.1 s . The first error (exp.) is the systematic experimental uncertainly, the statistical error is negligible. The other errors are due to hadronization (hadr.), renormalization scale (scale) uncertainties, and differences between the calculated second order corrections (theor.).
Statistical errors are equal to or less than 0.6 pct in each bin. There is also a 4 pct systematic uncertainty.
ALPHA_S from the EEC measurement.. The first error given is the experimental error which is mainly the overall systematic uncertainty: the first (DSYS) error is due to hadronization, the second to the renormalization scale, and the third differences between the calculated and second order corrections.
ALPHA_S from the AEEC measurement.. The first error given is the experimental error which is mainly the overall systematic uncertainty: the first (DSYS) error is due to hadronization, the second to the renormalization scale, and the third differences between the calculated and second order corrections.
From an analysis of multi-hadron events from Z 0 decays, values of the strong coupling constant α s ( M 2 Z 0 )=0.131±0.006 (exp)±0.002(theor.) and α s ( M z 0 2 ) = −0.009 +0.007 (exp.) −0.002 +0.006 (theor.) are derived from the energy-energy correlation distribution and its asymmetry, respectively, assuming the QCD renormalization scale μ = M Z 0 . The theoretical error accounts for differences between O ( α 2 s ) calculations. A two parameter fit Λ MS and the renormalization scale μ leads to Λ MS =216±85 MeV and μ 2 s =0.027±0.013 or to α s ( M 2 Z 0 )=0.117 +0.006 −0.008 (exp.) for the energy-energy correlation distribution. The energy-energy correlation asymmetry distribution is insensitive to a scale change: thus the α s value quoted above for this variable includes the theoretical uncertainty associated with the renormalization scale.
Data are at the hadron level, unfolded for initial-state radiation and for detector acceptance and resolution. Note that the systematic errors between bins are correlated.
Alpha-s determined from the EEC measurements. The systematic error is an error in the theory.
Alpha-s determined from the AEEC measurements. The systematic error is an error in the theory.
We have studied the energy-energy angular correlations in hadronic final states from Z 0 decay using the DELPHI detector at LEP. From a comparison with Monte Carlo calculations based on the exact second order QCD matrix element and string fragmentation we find that Λ (5) MS =104 +25 -20 ( stat. ) +25 -20( syst. ) +30 00 ) theor. ) . MeV, which corresponds to α s (91 GeV)=0.106±0.003(stat.)±0.003(syst.) +0.003 -0.000 (theor). The theoretical error stems from different choices for the renormalization scale of α s . In the Monte Carlo simulation the scale of α s as well as the fragmentation parameters have been optimized to described reasonably well all aspects of multihadron production.
Data requested from the authors.
Values of LAMBDA-MSBAR(5) and ALPHA-S(91 GeV) deduced from the EEC measurements. The second systematic error is from the theory.
We have studied the energy-energy correlation in e+e− annihilation into hadrons at √s =29 GeV using the Mark II detector at the SLAC storage ring PEP. We find to O(αs2) that αs=0.158±0.003±0.008 if hadronization is described by string fragmentation. Independent fragmentation schemes give αs=0.10–0.14, and give poor agreement with the data. A leading-log shower fragmentation model is found to describe the data well.
Correlation data from the original PEP-5 detector.
Correlation Asymmetry data from the original PEP-5 detector.
Correlation data from the upgraded detector.
We present data on energy-energy correlations (EEC) and their related asymmetry (AEEC) ine+e− annihilation in the centre of mass energy range 12<W≦46.8 GeV. The energy and angular dependence of the EEC in the central region is well described byOαs2 QCD plus a fragmentation term proportional to\({1 \mathord{\left/ {\vphantom {1 {\sqrt s }}} \right. \kern-\nulldelimiterspace} {\sqrt s }}\). BareO(α)s2 QCD reproduces our data for the large angle region of the AEEC. Nonperturbative effects for the latter are estimated with the help of fragmentation models. From various analyses using different approximations, we find that values for\(\Lambda _{\overline {MS} } \) in the range 0.1–0.3 GeV give a good description of the data. We also compare analytical calculations in QCD for the EEC in the back-to-back region to our data. The theoretical predictions describe well both the angular and energy dependence of the data in the back-to-back region.
Correlation function binned in cos(chi).
Correlation function binned in cos(chi).
Correlation function binned in cos(chi).
The energy-energy correlation cross section for hadrons produced in electron-positron annihilation at a center-of-mass energy of 29 GeV has been measured with the MAC detector at SLAC. The result is corrected for the effects of detector resolution, acceptance, and initial-state radiation. The correlation is measured in two independent ways on the same data sample: the energy weights and angles are obtained either from the energy flow in the finely segmented total absorption calorimeters or from the momenta of charged tracks in the central drift chamber. This procedure helps reduce systematic errors by cross-checking the effects of the detector on the measurement, particularly important because the corrections depend on complex Monte Carlo simulations. The results are compared with the predictions of Monte Carlo models of complete second-order perturbative quantum chromodynamics and fragmentation, with the following conclusions: (1) fitting the asymmetry for large correlation angles gives values for αS of 0.120±0.006 in perturbation theory, 0.185±0.013 in the Lund string model, and values which vary from 0.105 to 0.140 (±0.01) in the incoherent jet models, depending on the gluon fragmentation scheme and the algorithm used for momentum conservation; and (2) the string fragmentation model provides a satisfactory description of the measured energy-energy correlation cross section, whereas incoherent jet formation does not.
VALUES FOR THE ASSYMETRY ARE GIVEN ALSO.
Energy-energy-correlations (EEC) have been measured with the JADE detector at c.m. energies of 14 GeV, 22 GeV and in the region 29 GeV<Ecm<36 GeV. Corrected results are presented of EEC and their asymmetry, which can be directly compared to theoretical predictions. At 〈Ecm〉=34 GeV a comparison with second order QCD predictions yields good agreement for the string model fragmentation resulting in a value of the strong coupling constant αs=0.165±0.01 (stat.). The independent fragmentation models, which yield values of αs between 0.10 and 0.15 depending on the treatment of energy and momentum conservation and of the gluon splitting, do not provide a satisfactory description of the data over the full angular range.
TABLES GIVEN HERE CONTAIN SELF CORRELATION. THIS IS SUBTRACTED IN THE FIGURE.
VALUE OF ASSYMETRY IN CORRELATIONS.
No description provided.
Hadronic events obtained with the CELLO detector at PETRA are compared with second order QCD predictions using different models for the fragmentation of quarks and gluons into hadrons. We find that the model dependence in the determination of the strong coupling constant persists when going from first to second order QCD calculations.
ASYMMETRY FOR DATA CORRECTED WITH IF MODEL (ALPHA-S=0.12).
ASSYMETRY FOR DATA CORRECTED WITH SF MODEL (ALPHA-S=0.19).
No description provided.
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