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Precision Electroweak Measurements on the Z Resonance

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Precision Electroweak Measurements on the Z Resonance EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH STANFORD LINEAR ACCELERATOR CENTER CERN-PH-EP/2005-041 SLAC-R-774 hep-ex/0509008 7 September 2005 Precision Electroweak Measurements on the Z Resonance The ALEPH, DELPHI, L3, OPAL, SLD Collaborations,1 the LEP Electroweak Working Group,2 the SLD Electroweak and Heavy Flavour Groups arXiv:hep-ex/0509008v3 27 Feb 2006 Accepted for publication in Physics Reports Updated: 20 February 2006 1See Appendix A for the lists of authors. 2Web access at http://www.cern.ch/LEPEWWG 1 Abstract We report on the final electroweak measurements performed with data taken at the Z resonance by the experiments operating at the electron-positron colliders SLC and LEP. The data consist of 17 million Z decays accumulated by the ALEPH, DELPHI, L3 and OPAL experiments at LEP, and 600 thousand Z decays by the SLD experiment using a polarised beam at SLC. The measurements include cross-sections, forward-backward asymmetries and polarised asymmetries. The mass and width of the Z boson, mZ and ΓZ, and its couplings to fermions, for example the ρ parameter and the effective electroweak mixing angle for leptons, are precisely measured: m = 91.1875 0.0021 GeV Z ± Γ = 2.4952 0.0023 GeV Z ± ρ = 1.0050 0.0010 ℓ ± sin2 θlept = 0.23153 0.00016 . eff ± The number of light neutrino species is determined to be 2.9840 0.0082, in agreement with ± the three observed generations of fundamental fermions. The results are compared to the predictions of the Standard Model. At the Z-pole, elec- troweak radiative corrections beyond the running of the QED and QCD coupling constants are observed with a significance of five standard deviations, and in agreement with the Standard Model. Of the many Z-pole measurements, the forward-backward asymmetry in b-quark pro- duction shows the largest difference with respect to its Standard Model expectation, at the level of 2.8 standard deviations. Through radiative corrections evaluated in the framework of the Standard Model, the Z-pole +13 data are also used to predict the mass of the top quark, mt = 173 10 GeV, and the mass of the − W boson, mW = 80.363 0.032 GeV. These indirect constraints are compared to the direct measurements, providing± a stringent test of the Standard Model. Using in addition the direct measurements of mt and mW, the mass of the as yet unobserved Standard Model Higgs boson is predicted with a relative uncertainty of about 50% and found to be less than 285 GeV at 95% confidence level. Keywords: Electron-positron physics, electroweak interactions, decays of heavy intermediate gauge bosons, fermion-antifermion production, precision measurements at the Z resonance, tests of the Standard Model, radiative corrections, effective coupling constants, neutral weak current, Z boson, W boson, top quark, Higgs boson. PACS: 12.15.-y, 13.38.-b, 13.66.-a, 14.60.-z, 14.65.-q, 14.70.-e, 14.80.-j. 2 Acknowledgements We would like to thank the CERN accelerator divisions for the efficient operation of the LEP accelerator, the precise information on the absolute energy scale and their close cooperation with the four experiments. The SLD collaboration would like to thank the SLAC accelerator department for the efficient operation of the SLC accelerator. We would also like to thank members of the CDF, DØ, NuTeV and E-158 Collaborations for making results available to us and for useful discussions concerning their combination. Finally, the results and their interpre- tation within the Standard Model would not have been possible without the close collaboration of many theorists. 3 Contents 1 Introduction 14 1.1 LEPandSLCData.................................. 14 1.1.1 LEP ...................................... 16 1.1.2 SLC ...................................... 19 1.2 LEP/SLCDetectors ................................ 21 1.3 BasicMeasurements ............................... .. 23 1.4 StandardModelRelations . .... 26 + 1.5 The Process e e− ff................................ 30 → 1.5.1 Cross-Sections and Partial Widths . ..... 31 1.5.2 Invisible Width and Number of Neutrinos . ..... 35 1.5.3 AsymmetryandPolarisation. ... 35 1.5.4 Relating Theory and Experiment . ... 39 1.6 Interpretation and Impact of the Results . ......... 41 2 The Z Lineshape and the Leptonic Forward-Backward Asymmetries 45 2.1 Introduction.................................... .. 45 2.2 Measurements of Total Cross-Sections and Forward-Backward Asymmetries . 47 2.2.1 EventSelection ................................ 47 2.2.2 Cross-Section Measurements . .... 49 2.2.3 Measurements of the Lepton Forward-Backward Asymmetries ...... 52 2.2.4 ExperimentalSystematicErrors . ..... 54 2.2.5 EnergyCalibration .. .. .. 55 2.3 ExperimentalResults ............................. ... 60 2.4 CommonUncertainties ............................. .. 64 2.4.1 Energy Calibration Uncertainties . ...... 65 2.4.2 Uncertainties Related to the t-Channel ................... 65 2.4.3 Luminosity Uncertainties . ... 66 2.4.4 TheoryUncertainties . .. .. 67 2.5 CombinationofResults ............................ ... 69 2.5.1 MultipleZ-MassFits . .. .. 70 2.5.2 Shifts for Halved Experimental Errors . ...... 70 2.5.3 Influence of the γ–ZInterferenceTerm . 72 2.5.4 Direct Standard Model Fits to Cross-Sections and Asymmetries . 73 2.6 CombinedResults ................................. 74 4 3 Measurement of Left-Right and Lepton Asymmetries at the SLC 77 3.1 Left-Right Asymmetry Measurements . ....... 77 3.1.1 ElectronPolarisationattheSLC . .... 78 3.1.2 PolarimetryattheSLC . .. .. 78 3.1.3 EnergySpectrometry . 85 3.1.4 EventSelection ................................ 86 3.1.5 ControlofSystematicEffects . ... 87 3.1.6 Results..................................... 89 3.2 Lepton Asymmetry Measurements . ..... 93 3.2.1 AnalysisMethod ............................... 93 3.2.2 SystematicErrors.............................. 95 3.2.3 Results..................................... 96 3.3 CombinedResults................................. .. 97 4 The Tau Polarisation Measurements 98 4.1 Introduction.................................... .. 98 4.2 ExperimentalMethods . .. .. .. ... 99 4.3 SystematicErrors................................ 109 4.3.1 Decay-Independent Systematic Uncertainties . ..........110 4.3.2 Decay-Dependent Systematic Uncertainties . .........111 4.4 Results......................................... 114 5 Results from b and c Quarks 118 5.1 Introduction.................................... 118 5.2 HeavyFlavourTaggingMethods. 119 5.2.1 LifetimeTagging ............................... 120 5.2.2 CombinedLifetimeTag. 122 5.2.3 LeptonTagging ................................125 5.2.4 D-MesonTags.................................126 5.3 PartialWidthMeasurements. 130 5.3.1 Rb Measurements...............................131 5.3.2 Rc Measurements ...............................132 5.4 AsymmetryMeasurements . 134 5.4.1 LeptonandD-MesonMeasurements. 137 5.4.2 JetandVertexCharge ............................ 137 5.4.3 Kaons .....................................139 5.4.4 Asymmetry Measurements used in the Combination . .......139 5.5 AuxiliaryMeasurements . 140 5.6 External Inputs to the Heavy Flavour Combination . ..........140 5.6.1 FragmentationofHeavyQuarks . 141 5.6.2 HeavyQuarksfromGluonSplitting . 143 5.6.3 Multiplicities in Heavy Flavour Decays . .......143 5.6.4 HeavyFlavourLifetimes . 144 5.6.5 Charmed Hadron Decays to Exclusive Final States . .......145 5.6.6 Heavy Flavour Leptonic Decays . 145 5.6.7 Hemisphere Correlations in Double-Tag Methods . ........147 5.6.8 Light Quark Background in Lifetime Tagged Samples . ........148 5.7 Corrections to the Electroweak Observables . ..........149 5 5.7.1 Corrections to Rb and Rc ..........................149 5.7.2 QCD Corrections to the Forward-Backward Asymmetries .........149 5.7.3 Other Corrections to the Asymmetries . 150 5.8 CombinationProcedure . .. .. .. 151 5.9 Results......................................... 153 6 Inclusive Hadronic Charge Asymmetry 164 6.1 Asymmetry of Flavour-Inclusive Hadronic Events . ...........164 6.2 SystematicUncertainties . ......166 6.3 CombinationProcedure . .. .. .. 167 6.4 Combined Results and Discussion . ......167 7 Z Boson Properties and Effective Couplings 170 7.1 SummaryofZ-PoleResults . 170 7.1.1 Overview ...................................170 7.2 Z-Boson Decay Widths and Branching Fractions . .........172 7.2.1 Z-BosonDecayParameters. 172 7.2.2 Invisible Width and Number of Light Neutrino Species . .........172 7.3 Effective Couplings of the Neutral Weak Current . .........175 7.3.1 The Asymmetry Parameters .......................176 Af 7.3.2 The Effective Coupling Constants . 179 7.3.3 The ρf Parameters and the Effective Electroweak Mixing Angles . 184 7.3.4 The Leptonic Effective Electroweak Mixing Angle . ........184 7.3.5 Discussion...................................188 7.4 Sensitivity to Radiative Corrections Beyond QED . ...........189 8 Constraints on the Standard Model 192 8.1 ParametersoftheStandardModel . 192 8.2 HadronicVacuumPolarisation. ......194 8.3 AdditionalMeasurements . 195 8.3.1 MassoftheTopQuark............................195 8.3.2 MassandWidthoftheWBoson . 195 8.3.3 Measurements at Low Momentum Transfer . 196 8.4 Parametric and Theoretical Uncertainties . ...........197 8.4.1 ParameterDependence . 197 8.4.2 TheoreticalUncertainties. 201 8.5 AnalysisProcedure ............................... 208 8.5.1 Treatment of Systematic Uncertainties . .......209 8.6 StandardModelAnalyses . 209 8.6.1 Z-PoleResults................................. 209 8.6.2 TheMassoftheTopQuarkandoftheWBoson . 211 8.6.3
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