The forward-backward asymmetry of bottom quarks is measured with statistics of approximately 80 000 hadronic Z 0 decays produced in e + e − collisions at a centre of mass energy of √ s ≈ M z . The tagging of b quark events has been performed using the semileptonic decay channel b→X+ μ . Because the asymmetry depends on the weak coupling, this leads to a precise measurement of the electroweak mixing angle sin 2 θ w . The experimental result is A FB b = 0.115±0.043(stat.)±0.013(syst.). After correcting the value for the B 0 B 0 mixing this becomes A FB b =0.161±0.060(stat.)±0.021(syst.) corresponding to sin 2 θ W MS =0.221±0.011( stat. )±0.004( syst. ) .
Experimentally measured asymmetry.
Asymmetry corrected for mixing using mixing parameter 0.143 +- 0.023.
SIN2TW measured in MSBAR scheme.
From measurements of the cross sections for e + e − → hadrons and the cross sections and forward-backward charge-asymmetries for e e −→ e + e − , μ + μ − and π + π − at several centre-of-mass energies around the Z 0 pole with the DELPHI apparatus, using approximately 150 000 hadronic and leptonic events from 1989 and 1990, one determines the following Z 0 parameters: the mass and total width M Z = 91.177 ± 0.022 GeV, Γ Z = 2.465 ± 0.020 GeV , the hadronic and leptonic partial widths Γ h = 1.726 ± 0.019 GeV, Γ l = 83.4 ± 0.8 MeV, the invisible width Γ inv = 488 ± 17 MeV, the ratio of hadronic over leptonic partial widths R Z = 20.70 ± 0.29 and the Born level hadronic peak cross section σ 0 = 41.84±0.45 nb. A flavour-independent measurement of the leptonic cross section gives very consistent results to those presented above ( Γ l = 83.7 ± 0.8 rmMeV ). From these results the number of light neutrino species is determined to be N v = 2.94 ±0.10. The individual leptonic widths obtained are: Γ e = 82.4±_1.2 MeV, Γ u = 86.9±2.1 MeV and Γ τ = 82.7 ± 2.4 MeV. Assuming universality, the squared vector and axial-vector couplings of the Z 0 to charged leptons are: V ̄ l 2 = 0.0003±0.0010 and A ̄ l 2 = 0.2508±0.0027 . These values correspond to the electroweak parameters: ϱ eff = 1.003 ± 0.011 and sin 2 θ W eff = 0.241 ± 0.009. Within the Minimal Standard Model (MSM), the results can be expressed in terms of a single parameter: sin 2 θ W M ̄ S = 0.2338 ± 0.0027 . All these values are in good agreement with the predictions of the MSM. Fits yield 43< m top < 215 GeV at the 95% level. Finally, the measured values of Γ Z and Γ inv are used to derived lower mass bounds for possible new particles.
Cross section from analysis I based on energy of charged particles. Additional 1.0 pct normalisation uncertainty.
Cross section from analysis II based on calorimeter energies. Additional 1.1 pct normalisation uncertainty.
Cross sections within the polar angle range 44 < THETA < 136 degrees and acollinearity < 10 degrees.. Overall systematic error 1.2 pct not included.
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DATA FROM 1989 RUN. The cross section are quoted with their statistical and point-to-point systematic uncertainty of both the multihadron acceptance and the luminosity calculation.
DATA FROM 1990 RUN. The cross section are quoted with their statistical and point-to-point systematic uncertainty of both the multihadron acceptance and the luminosity calculation.
Cross sections corrected for the effects of efficiency and kinematic cuts and background. Data from 1989 run, reanalysed.
Measurements of the cross section and forward-backward asymmetry for the reaction e + e − → μ + μ − using the DELPHI detector at LEP are presented. The data come from a scan around the Z 0 peak at seven centre of mass energies, giving a sample of 3858 events in the polar angle region 22° < θ < 158°. From a fit to the cross section for 43° < θ < 137°, a polar angle region for which the absolute efficiency has been determined, the square root of the product of the Z 0 → e + e − and Z 0 → μ + μ − partial widths is determined to be (Γ e Γ μ ) 1 2 = 85.0 ± 0.9( stat. ) ± 0.8( syst. ) MeV . From this measurement of the partial width, the value of the effective weak mixing angle is determined to be sin 2 ( θ w ) = 0.2267 ± 0.0037 . The ratio of the hadronic to muon pair partial widths is found to be Γ h / Γ μ = 19.89 ± 0.40(stat.) ± 0.19(syst.). The forward-backward asymmetry at the resonance peak energy E CMS = 91.22 GeV is found to be A FB = 0.028 ± 0.020(stat.) ± 0.005(syst.). From a combined fit to the cross section and forward-backward asymmetry data, the products of the electron and muon vector and axial-vector coupling constants are determined to be V e V μ = 0.0024 ± 0.0015(stat.) ± 0.0004(syst.) and A e A μ = 0.253 ± 0.003(stat.) ± 0.003 (syst.). The results are in good agreement with the expectations of the minimal standard model.
Fully corrected cross sections.
Forward-backward asymmetries corrected to full solid angle, but not for cuts on momenta and acollinearity.
Effective weak mixing angle.
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 .
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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