Measurement of the photon structure function F2 (gamma) in the reaction e+ e- ---> e+ e- + hadrons at LEP

The OPAL collaboration Akers, R. ; Alexander, G. ; Allison, John ; et al.
Z.Phys.C 61 (1994) 199-208, 1994.
Inspire Record 358863 DOI 10.17182/hepdata.48474

We present measurements of the hadronic photon structure functionF2γ(x), in twoQ2 ranges with mean values of 5.9 GeV2 and 14.7 GeV2. The data were taken by the OPAL experiment at LEP, with\(\sqrt s\) close to theZ0 mass and correspond to an integratede+e− luminosity of 44.8 pb−1. In the context of a QCD-based model we find the quark transverse momentum cutoff separating the vector meson dominance (VMD) and perturbative QCD regions to be 0.27±0.10 GeV. We confirm that there is a significant pointlike component of the photon when the probe photon hasQ2>4 GeV2. Our measurements extend to lower values ofx than any previous experiment, and no increase ofF2γ(x) is observed.

2 data tables

Additional overall systematic error 5.9% not included.

Additional overall systematic error 5.9% not included.


The Forward - backward asymmetry of e+ e- ---> b anti-b and e+ e- ---> c anti-c using leptons in hadronic Z0 decays

The OPAL collaboration Acton, P.D. ; Akers, R. ; Alexander, G. ; et al.
Z.Phys.C 60 (1993) 19-36, 1993.
Inspire Record 356097 DOI 10.17182/hepdata.14320

The forward-backward asymmetries of$$e^ + e^ - \to Z^0 \to b\bar b and e^ + e^ - \to Z^0 \to c\bar c$$

5 data tables

Measurement of the asymmetry in b-quark production on the Z0 peak using a two parameter fit, neglecting the effects of B0-BBAR0 mixing.

Measurement of the asymmetry in b-quark production on the Z0 peak using a two parameter fit and correcting for B0-BBAR0 mixing. The second systematic error is due to the uncertainty of the mixing factor.

Measurement of the asymmetry in c-quark production on the Z0 peak using a two parameter fit.

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A Determination of alpha-s (M (Z0)) at LEP using resummed QCD calculations

The OPAL collaboration Acton, P.D. ; Alexander, G. ; Allison, John ; et al.
Z.Phys.C 59 (1993) 1-20, 1993.
Inspire Record 354188 DOI 10.17182/hepdata.14427

The strong coupling constant, αs, has been determined in hadronic decays of theZ0 resonance, using measurements of seven observables relating to global event shapes, energy correlatio

7 data tables

Data corrected for finite acceptance and resolution of the detector and for intial state photon radiation. No corrections for hadronic effects are applied.. Errors include statistical and systematic uncertainties, added in quadrature.

Data corrected for finite acceptance and resolution of the detector and for intial state photon radiation. No corrections for hadronic effects are applied.. Errors include statistical and systematic uncertainties, added in quadrature.

Data corrected for finite acceptance and resolution of the detector and for intial state photon radiation. No corrections for hadronic effects are applied.. Errors include statistical and systematic uncertainties, added in quadrature.

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Evidence for chain - like production of strange baryon pairs in jets

The OPAL collaboration Acton, P.D. ; Alexander, G. ; Allison, John ; et al.
Phys.Lett.B 305 (1993) 415-427, 1993.
Inspire Record 353460 DOI 10.17182/hepdata.48367

The production dynamics of baryon-antibaryon pairs are investigated using hadronic Z 0 decays, recorded with the OPAL detector, which contain at least two identified Λ baryons. The rapidly difference for Λ Λ pairs shows the correlations expected from models with a chain-like production of baryon-antibaryon pairs. If the baryon number of a Λ is compensated by a Λ , the Λ is found with a probability of 53% in an interval of ±0.6 around the Λ rapidity. This correlation strength is weaker than predicted by the Herwig Monte Carlo and the Jetset Monte Carlo with a production chain of baryon-antibaryon, and stronger than predicted by the UCLA model. The observed rapidity correlations can be described by the Jetset Monte Carlo with a dominant production chain of baryon-meson-antibaryon, the popcorn mechanism. In addition to the short range correlations, one finds an indication of a correlation of Λ Λ pairs in opposite hemispheres if both the Λ and the Λ have large rapidities. Such long range correlations are expected if the primary quark flavours are compensated in opposite hemispheres and if these quarks are found in energetic baryons. Rates for simultaneous baryon and strangeness number compensation for Λ Λ , Ξ − Ξ + and Ξ − Λ ( Λ + Λ ) are measured and compared with different Monte Carlo models.

17 data tables

No description provided.

Opposite and same baryon number invariant PI P mass distribuition for additional LAMBDA(LAMBDABAR) candidates in events with one identified LAMBDA(LAMBDABAR). CT.= Data read from plot.

Opposite and same baryon number invariant PI P mass distribuition for additional LAMBDA(LAMBDABAR) candidates in events with one identified XI-(XIBAR+). CT.= Data read from plot.

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Precision measurements of the neutral current from hadron and lepton production at LEP

The OPAL collaboration Acton, P.D. ; Alexander, G. ; Allison, John ; et al.
Z.Phys.C 58 (1993) 219-238, 1993.
Inspire Record 352696 DOI 10.17182/hepdata.14495

New measurements of the hadronic and leptonic cross sections and of the leptonic forward-backward asymmetries ine+e− collisions are presented. The analysis includes data recorded up to the end of 1991 by the OPAL experiment at LEP, with centre-of-mass energies within ±3 GeV of the Z0 mass. The results are based on a recorded total of 454 000 hadronic and 58 000 leptonic events. A model independent analysis of Z0 parameters based on an extension of the improved Born approximation is presented leading to test of lepton universality and an interpretation of the results within the Standard Model framework. The determination of the mass and width of the Z0 benefit from an improved understanding of the LEP energy calibration.

9 data tables

Statistical and systematic point-to-point errors included. There is an additional 0.2 pct overall systematic uncertainty.

Systematic error of 0.45 pct not included.

Systematic error of 0.25 pct not included.

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A Study of differences between quark and gluon jets using vertex tagging of quark jets

The OPAL collaboration Acton, P.D. ; Alexander, G. ; Allison, John ; et al.
Z.Phys.C 58 (1993) 387-404, 1993.
Inspire Record 352789 DOI 10.17182/hepdata.48418

Quark and gluon jets with equal energies are identified in three-jet hadronicZ0 events, using reconstructed secondary vertices from heavy quark decay in conjunction with energy orderi

1 data table

No description provided.


A Measurement of K*+- (892) production in hadronic Z0 decays

The OPAL collaboration Acton, P.D. ; Alexander, G. ; Allison, John ; et al.
Phys.Lett.B 305 (1993) 407-414, 1993.
Inspire Record 342766 DOI 10.17182/hepdata.28930

Measurements are presented of the inclusive cross section for K ∗ (892) ± production in hadronic decays of the Z 0 using a sample of about half a million events recorded with the OPAL experiment at LEP. Charged K ∗ mesons are reconstructed in the decay channel K 0 S π ± . A mean rate of 0.72±0.02±0.08 K ∗ mesons per hadronic event is found. Comparison of the results with predictions of the JETSET and HERWIG models shows that JETSET overestimates the K ∗± production cross section while HERWIG is consistent with the data.

2 data tables

No description provided.

No description provided.


QCD coherence studies using two particle azimuthal correlations

The OPAL collaboration Acton, P.D. ; Alexander, G. ; Allison, John ; et al.
Z.Phys.C 58 (1993) 207-218, 1993.
Inspire Record 343082 DOI 10.17182/hepdata.14494

From a sample of 146900 hadronicZ0 decays recorded by the OPAL detector at LEP, we have studied the azimuthal correlations of particles in hadronic events. It is expected that these correlations are sensitive to interference effects in QCD. We have compared the data to QCD Monte Carlo models which include and which do not include interference effects. We find that the distributions of azimuthal correlations are not reproduced by the parton shower models we have tested unless interference effects are included, no matter which hadronisation scheme is used.

2 data tables

Corrected data for the EMMC.

Corrected data for the TPAC.


Studies of strong and electroweak interactions using final state photon emission in hadronic Z0 decays

The OPAL collaboration Acton, P.D. ; Alexander, G. ; Allison, John ; et al.
Z.Phys.C 58 (1993) 405-418, 1993.
Inspire Record 343181 DOI 10.17182/hepdata.52379

The cross section and jet rates ofZ0 decays into photons and quarks are compared with matrix element Monte Carlos ofO(ααs). Good agreement is found between data and theoretical predic

4 data tables

Corrected number of hadronc events that have a final state photon per 1000 multhadronic Z0 decays, using the E0 scheme.

Corrected number of hadronc events that have a final state photon per 1000 multhadronic Z0 decays, using the Durham scheme.

Corrected number of events that have a final state photon with 1, 2, 3, or more jets per 1000 multhadronic Z0 decays, using the E0 scheme.

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A Measurement of the forward - backward charge asymmetry in hadronic decays of the Z0

The OPAL collaboration Acton, P.D. ; Alexander, G. ; Allison, J. ; et al.
Phys.Lett.B 294 (1992) 436-450, 1992.
Inspire Record 336774 DOI 10.17182/hepdata.29004

We present a measurement of the forward-backward charge asymmetry in hadronic decays of the Z 0 using data collected with the OPAL detector at LEP. The forward-backward charge asymmetry was measured using a weight function method which gave the number of forward events on a statistical basis. In a data sample of 448 942 hadronic Z 0 decays, we have observed a charge asymmetry of A h = 0.040±0.004 (stat.)±0.006 (syst.)±0.002 (B 0 B 0 mix.), taking into account the effect of B 0 B 0 mixing. In the framework of the standard model, this asymmetry corresponds to an effective weak mixing angle averaged over five quark flavours of sin 2 θ W = 0.2321 ± 0.0017 ( stat. ) ± 0.0027 ( syst. ) ± 0.0009 (B 0 B 0 mix.). The result agrees with the value obtained from the Z 0 line shape and lepton pair forward-backward asymmetry.

3 data tables

No description provided.

The second systematic error is due to the uncertainty in the correction for B.BBAR mixing which had been applied to the data.

The second systematic error is due to the uncertainty in the correction for B.BBAR mixing which had been applied to the data.


A Measurement of strange baryon production in hadronic Z0 decays

The OPAL collaboration Acton, P.D. ; Alexander, G. ; Allison, J. ; et al.
Phys.Lett.B 291 (1992) 503-518, 1992.
Inspire Record 336771 DOI 10.17182/hepdata.29036

The production of the octet and decuplet baryons Λ, Ξ − , Σ (1385) ± , Ξ(1530) 0 and Ω − and the corresponding antibaryons has been measured in a sample of 485 000 hadronic Z 0 decays. Results on differential and integrated cross sections are presented. The differential cross section of Λ baryons is found to be softer than the one predicted by the Jetset and Herwig Monte Carlo generators. The measured decuplet yields are found to disagree with the simple diquark picture where only one tuning parameter for spin 1 diquarks is used. Comparisons of the momentum spectra for Λ and Ξ − with the predictions of an analytical QCD formula are also presented.

13 data tables

No description provided.

No description provided.

No description provided.

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Evidence for b flavored baryon production in Z0 decays at LEP

The OPAL collaboration Acton, P.D. ; Alexander, G. ; Allison, J. ; et al.
Phys.Lett.B 281 (1992) 394-404, 1992.
Inspire Record 333300 DOI 10.17182/hepdata.48511

We observe evidence for the production of b-flavoured baryons in decays of the Z 0 boson with the OPAL detector at LEP. We find 68 Λl − , Λ l + candidates in 458 583 hadronic Z 0 decays. We interpret this as a signal of 55 ± 9 +0.3 −3.1 events from the semi-leptonic decays of b baryons. Assuming weakly decaying b baryons produced in Z 0 decays are mostly Λ b particles, we measure the product branching ratio (Γ b b /Γ had ) f ( b →Λ b ) B (Λ b →Λl − v X ) , averaged over the electron and muon channels, to be (6.2±1.0±1.5)×10 −4 .

1 data table

FD is considered as a quark fragmentation fraction. Charge conjugated state is understood.


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.

2 data tables

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.


A Measurement of photon radiation in lepton pair events from Z0 decays

The OPAL collaboration Acton, P.D. ; Alexander, G. ; Allison, J. ; et al.
Phys.Lett.B 273 (1991) 338-354, 1991.
Inspire Record 319674 DOI 10.17182/hepdata.48520

We have measured the photon yield in lepton pair events recorded by the OPAL detector in a data sample corresponding to an integrated luminosity of 7.1 pb −1 at centre-of-mass energies between 88 GeV and 94 GeV. The results are compared to QED expectations for initial and final state photon radiation. No anomalous photon yield has been found, and stringent limits on the branching ratio for exotic radiative three body Z 0 decays into a photon and a pair of leptons are obtained. We also place limits on possible Z 0 decays into a photon and a resonance X with subsequent decays of X into a pair of leptons. Acollinear μ + μ − events with missing momentum along the beam direction are identified as events with hard initial state photon radiation and used to measure an average cross section of 15 ± 8 6 pb for e + e − annihilation into μ + μ − , in the so far untested range of centre-of-mass energies between 60 GeV and 84 GeV. This value is consistent with a cross section of 24 pb, expected from Z 0 and photon exchange.

1 data table

No description provided.


Analysis of Z0 couplings to charged leptons

The OPAL collaboration Akrawy, M.Z. ; Alexander, G. ; Allison, J. ; et al.
Phys.Lett.B 247 (1990) 458-472, 1990.
Inspire Record 297139 DOI 10.17182/hepdata.29630

The couplings of the Z 0 to charged leptons are studied using measurements of the lepton pair cross sections and forward-backward asymmetries at centre of mass energies near to the mass of the Z 0 . The data are consistent with lepton universality. Using a parametrisation of the lepton pair differential cross section which assumes that the Z 0 has only vector and axial couplings to leptons, the charged leptonic partial decay width of the Z 0 is determined to be Г ol+ol− = 83.1±1.9 MeV and the square of the product of the effective axial vector and vector coupling constants of the Z 0 to charged leptons to be a ̌ 2 ol v ̌ 2 ol = 0.0039± 0.0083 , in agreement with the standard model. A parametrisation in the form of the improved Born approximation gives effective leptonic axial vector and vector coupling constants a ̌ 2 ol = 0.998±0.024 and v ̌ 2 ol = 0.0044±0.0083 . In the framework of the standard model, the values of the parameters ϱ z and sin 2 θ w are found to be 0.998±0.024 and 0.233 +0.045 −0.012 respectively. Using the relationship in the minimal standard model between ϱ z and sin 2 θ w , the results sin 2 θ SM w = 0.233 +0.007 −0.006 is obtained. Our previously published measurement of the ratio of the hadronic to the leptonic partial width of the Z 0 is update: R z = 21.72 +0.71 −0.65 .

6 data tables

Cross sections corrected for the effects of efficiency and kinematic cuts. Errors have systematic effects folded.

Acceptance corrected cross sections. Statistical errors only.

Acceptance corrected cross sections. Statistical errors only.

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A Study of coherence of soft gluons in hadron jets

The OPAL collaboration Akrawy, M.Z. ; Alexander, G. ; Allison, J. ; et al.
Phys.Lett.B 247 (1990) 617-628, 1990.
Inspire Record 297564 DOI 10.17182/hepdata.49561

We study the inclusive momentum distribution of charged particles in multihadronic events produced in e + e − annihilations at E CM ∼ M (Z 0 ). We find agreement with the analytical formulae for gluon production that include the phenomena of soft gluon interference. Using data from CM energies between 14 and 91 GeV, we study the dependence of the inclusive momentum distribution on the centre of momentum energy. We find that the analytical formulae describe the data over the entire energy range. Both the momentum distribution at a fixed energy and the change with energy are described by QCD shower Monte Carlo's which include either coherent gluon branchings or string fragmentation. Simple incoherent models with independent fragmentation fail to reproduce the energy dependence and momentum spectra.

1 data table

Statistical errors only. Overall systematic error of 5%.


A Measurement of Global Event Shape Distributions in the Hadronic Decays of the $\Z^0$

The OPAL collaboration Akrawy, M.Z. ; Alexander, G. ; Allison, John ; et al.
Z.Phys.C 47 (1990) 505-522, 1990.
Inspire Record 295613 DOI 10.17182/hepdata.15152

We present measurements of global event shape distributions in the hadronic decays of theZ0. The data sample, corresponding to an integrated luminosity of about 1.3 pb−1, was collected with the OPAL detector at LEP. Most of the experimental distributions we present are unfolded for the finite acceptance and resolution of the OPAL detector. Through comparison with our unfolded data, we tune the parameter values of several Monte Carlo computer programs which simulate perturbative QCD and the hadronization of partons. Jetset version 7.2, Herwig version 3.4 and Ariadne version 3.1 all provide good descriptions of the experimental distributions. They in addition describe lower energy data with the parameter values adjusted at theZ0 energy. A complete second order matrix element Monte Carlo program with a modified perturbation scale is also compared to our 91 GeV data and its parameter values are adjusted. We obtained an unfolded value for the mean charged multiplicity of 21.28±0.04±0.84, where the first error is statistical and the second is systematic.

9 data tables

Corrected Thrust distribution.

Corrected Major distribution.

Corrected Minor distribution.

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A Combined Analysis of the Hadronic and Leptonic Decays of the $\Z^0$

The OPAL collaboration Akrawy, M.Z. ; Alexander, G. ; Allison, J. ; et al.
Phys.Lett.B 240 (1990) 497-512, 1990.
Inspire Record 294808 DOI 10.17182/hepdata.29720

We report on a measurement of the mass of the Z 0 boson, its total width, and its partial decay widths into hadrons and leptons. On the basis of 25 801 hadronic decays and 1999 decays into electrons, muons or taus, selected over eleven energy points between 88.28 GeV and 95.04 GeV, we obtain from a combined fit to hadrons and leptons a mass of M z =91.154±0.021 (exp)±0.030 (LEP) GeV, and a total width of Γ z =2.536±0.045 GeV. The errors on M z have been separated into the experimental error and the uncertainty due to the LEP beam energy. The measured leptonic partial widths are Γ ee =81.2±2.6 MeV, Γ μμ =82.6± 5.8 MeV, and Γ ττ =85.7±7.1 MeV, consistent with lepton universality. From a fit assuming lepton universality we obtain Γ ℓ + ℓ − = 81.9±2.0 MeV. The hadronic partial width is Γ had =1838±46 MeV. From the measured total and partial widths a model independent value for the invisible width is calculated to be Γ inv =453±44 MeV. The errors quoted include both the statistical and the systematic uncertainties.

4 data tables

Errors are statistical and point to point systematic luminosity error of 1 pct.

Measured values of e+ e- --> e+ e- cross section.

Corrected cross section. Corrections are for t-channel effects and loss of acollinear events near the boundary of the acceptance.

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A Study of the Reaction $e^+ e^- \to \gamma \gamma$ at {LEP}

The OPAL collaboration Akrawy, M.Z. ; Alexander, G. ; Allison, J. ; et al.
Phys.Lett.B 241 (1990) 133-140, 1990.
Inspire Record 294809 DOI 10.17182/hepdata.29717

The pure QED reaction e + e − → γγ has been studied at centre of mass energies around the mass of the Z 0 boson using data recorded by the OPAL detector at LEP. The results are in good agreement with the QED prediction. Lower limits on the cutoff parameters of the modified electron propagator are found to be Λ + >89 GeV and Λ. The lower limit on the mass of an excited electron is 82 GeV assuming the coupling constant λ =1. Upper limits on the branching ratios of Z 0 → γγ , Z 0 → π 0 γ and Z 0 → ηγ are set at 3.7×10 −4 , 3.9×10 −4 and 5.8×10 −4 respectively. Two events from the reaction e + e − → γγγ have been observed, consistent with the QED prediction. An upper limit on the branching ratio of Z 0 → γγγ is set at 2.8×10 −4 . All the limits are given at 95% confidence level.

2 data tables

No description provided.

Data read from graph.


A Study of Jet Production Rates and a Test of QCD on the Z0 Resonance

The OPAL collaboration Akrawy, M.Z. ; Alexander, G. ; Allison, J. ; et al.
Phys.Lett.B 235 (1990) 389-398, 1990.
Inspire Record 283783 DOI 10.17182/hepdata.29753

Relative production rates of multijet hadronic final states of Z 0 boson decays, observed in e + e − annihilation around 91 GeV centre of mass energy, are presented. The data can be well described by analytic O( α s 2 ) QCD calculations and by QCD shower model calaculations with parameters as determined at lower energies. A first judgement of Λ MS and of the renormalization scale μ 2 in O( α s 2 ) QCD results in values similar to those obtained in the continuum of e + e − annihilations. Significant scaling violations are observed when the 3-jet fractions are compared to the corresponding results from smaller centre of mass energies. They can be interpreted as being entirely due tot the energy dependence of α s , as proposed by the nonabelian nature of QCD, The possibility of an energy independent coupling constant can be excluded with a significance of 5.7 standard deviations.

1 data table

Data are corrected for final acceptance and resolution of the detector. No explicit corrections for hadronisation effects are applied.


A Search for the Top and $b^\prime$ Quarks in Hadronic $\Z^0$ Decays

The OPAL collaboration Akrawy, M.Z. ; Alexander, G. ; Allison, J. ; et al.
Phys.Lett.B 236 (1990) 364-374, 1990.
Inspire Record 283784 DOI 10.17182/hepdata.29702

We report on a search for new quarks in hadronic Z° decays. From the event shape analysis of a data sample containing 2185 multihadronic annihilation events, we observe no evidence for the top or b' quarks. We derive limits for the top and b' quark masses under the assumption of various possible standard model and non-standard model decay schemes. Our search is sensitive to quark masses larger than 23 GeV/ c 2 ; it yields the following lower limits at a 95% confidence level: 44.5 GeV/ c 2 for the top quark mass and 45.2 GeV/ c 2 for the b′ quark mass.

1 data table

Measured event shape distributions - uncorrected.


Measurement of the Decay of the $\Z^0$ Into Lepton Pairs

The OPAL collaboration Akrawy, M.Z. ; Alexander, G. ; Allison, J. ; et al.
Phys.Lett.B 235 (1990) 379-388, 1990.
Inspire Record 283146 DOI 10.17182/hepdata.29723

We report on a measurement of the processes e + e − →e + e − , e + e − → μ + μ − , and e + e − → τ + τ − near the Z 0 pole. On the basis of 163 e + e − , 101 μ + μ − and 87 τ + τ − events we obtain Γ ee =89±4±4 MeV, Γ μμ =85±9±6 MeV and Γ ττ =87±10±8 MeV, compatible with the standard model. Combining these with our previous results on hadronic Z 0 decays, we find a hadronic width Γ had =1787±81±90 MeV and an invisible width Γ inv =552±85±71 MeV.

2 data tables

Statistical errors only.

Statistical errors only.


Measurement of the Z0 Mass and Width with the OPAL Detector at LEP

The OPAL collaboration Akrawy, M.Z. ; Alexander, G. ; Allison, J. ; et al.
Phys.Lett.B 231 (1989) 530-538, 1989.
Inspire Record 282821 DOI 10.17182/hepdata.29757

We report an experimental determination of the cross section for e + e − → hadrons from a scan around the Z 0 pole. On the basis of 4350 hadronic events collected over seven energy points between 89.26 GeV and 93.26 GeV we obtain a mass of m z =91.01±0.05±0.05 GeV, and a total decay width of Γ z =2.60±0.13 GeV. In the context of the standard model t these results imply 3.1 ± 0.4 neutrino generations.

1 data table

No description provided.