Analysis of the Energy Weighted Angular Correlations in Hadronic $e^+ e^-$ Annihilations at 22-{GeV} and 34-{GeV}

The CELLO collaboration Behrend, H.J. ; Chen, C. ; Fenner, H. ; et al.
Z.Phys.C 14 (1982) 95, 1982.
Inspire Record 12010 DOI 10.17182/hepdata.16413

Measurements of energy weighted angular correlations in electron positron annihilations at c.m. energies of 22 GeV and 34 GeV are presented.

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Measurements of Energy Correlations in $e^+ e^- \to$ Hadrons

The JADE collaboration Bartel, W. ; Becker, L. ; Bowdery, C. ; et al.
Z.Phys.C 25 (1984) 231, 1984.
Inspire Record 202784 DOI 10.17182/hepdata.1998

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.

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A Measurement of the Strong Coupling Constant $\alpha^- s$ to Complete Second Order

The Mark-J collaboration Adeva, B. ; Anderhub, H. ; Ansari, S. ; et al.
Phys.Lett.B 180 (1986) 181-184, 1986.
Inspire Record 231302 DOI 10.17182/hepdata.6535

The strong interaction coupling constant α s has been measured with a new method, the planar triple energy correlation in the reaction e + e - → hadrons at center-of-mass energies ranging from 14 GeV to 46.78 GeV. A complete second-order perturbative QCD calculation was used. Λ MS = 110 ± 30 −55 +70 MeV is found.

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Consistent measurements of alpha(s) from precise oriented event shape distributions.

The DELPHI collaboration Abreu, P. ; Adam, W. ; Adye, T. ; et al.
Eur.Phys.J.C 14 (2000) 557-584, 2000.
Inspire Record 522656 DOI 10.17182/hepdata.13245

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.

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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.

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On the Model Dependence of the Determination of the Strong Coupling Constant in Second Order {QCD} From $e^+ e^-$ Annihilation Into Hadrons

The CELLO collaboration Behrend, H.J. ; Fenner, H. ; Schachter, M.J. ; et al.
Phys.Lett.B 138 (1984) 311-316, 1984.
Inspire Record 195332 DOI 10.17182/hepdata.6634

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.

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A Study of Energy-energy Correlations in $e^+ e^-$ Annihilations at $\sqrt{s}=34$.6-{GeV}

The PLUTO collaboration Berger, Christoph ; Genzel, H. ; Lackas, W. ; et al.
Z.Phys.C 28 (1985) 365, 1985.
Inspire Record 215869 DOI 10.17182/hepdata.16029

We present high statistics measurements of the energy-energy correlation (EEC) and its related asymmetry (AEEC) ine+e− annihilation at a c.m. energy of 34.6 GeV. We find that the energy dependence as well as the large angle behaviour of the latter are well described by perturbative QCD calculations toOα(s2). Non-perturbative effects are estimated with the help of fragmentation models in which different jet topologies are separated using (ɛ, δ) cuts, and found to be small. The extracted values of\(\Lambda _{\overline {MS} }\) lie between 100 and 300 MeV.

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The Influence of Fragmentation Models on the Determination of the Strong Coupling Constant in $e^+ e^-$ Annihilation Into Hadrons

The CELLO collaboration Behrend, H.J. ; Chen, C. ; Fenner, H. ; et al.
Nucl.Phys.B 218 (1983) 269-288, 1983.
Inspire Record 179447 DOI 10.17182/hepdata.8172

Hadronic events obtained with the CELLO detector at PETRA were compared with first-order QCD predictions using two different models for the fragmentation of quarks and gluons, the Hoyer model and the Lund model. Both models are in reasonable agreement with the data, although they do not completely reproduce the details of many distributions. Several methods have been applied to determine the strong coupling constant α S . Although within one model the value of α S varies by 20% among the different methods, the values determined using the Lund model are 30% or more larger (depending on the method used) than the values determined with the Hoyer model. Our results using the Hoyer model are in agreement with previous results based on this approach.

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A Measurement of Energy-energy Correlations in $e^+ e^- \to$ Hadrons at $\sqrt{s}=29$-{GeV}

Fernandez, E. ; Ford, William T. ; Qi, N. ; et al.
Phys.Rev.D 31 (1985) 2724, 1985.
Inspire Record 202924 DOI 10.17182/hepdata.23586

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.

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An Improved measurement of alpha-s (M (Z0)) using energy correlations with the OPAL detector at LEP

The OPAL collaboration Acton, P.D. ; Alexander, G. ; Allison, J. ; et al.
Phys.Lett.B 276 (1992) 547-564, 1992.
Inspire Record 321657 DOI 10.17182/hepdata.29245

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.

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Measurement of Energy Correlations in $e^+ e^- \to$ Hadrons

Schlatter, D. ; Abrams, G.S. ; Amidei, D. ; et al.
Phys.Rev.Lett. 49 (1982) 521, 1982.
Inspire Record 171070 DOI 10.17182/hepdata.20563

Energy correlations have been measured with the MARK II detector at the PEP storage ring (Stanford Linear Accelerator Center) at c.m. energy of 29 GeV and are compared to first-order QCD predictions. Fragmentation processes are significant and limit the precision with which the first-order strong-coupling constant can be determined.

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