A Combination of Preliminary Electroweak Measurements and Constraints on the Standard Model

TL;DR

This work consolidates the full set of LEP and SLD electroweak measurements, spanning Z-pole precision data and LEP-II high-energy results, to yield a cohesive, high-precision test of the Standard Model. It employs a comprehensive averaging framework with full correlations to extract Z-pole parameters, heavy-flavour observables, and high-energy fermion-pair and photon-pair processes, then interprets these results in terms of effective couplings and SM constraints, including the hadronic vacuum polarization input. Key findings include a near-SM-consistent Z-pole picture with Nν ≈ 2.984 and precise R_b^0, R_c^0, A_FB^b, A_FB^c, A_b, and A_c values; and no significant deviations in LEP-II γγ and f f̄ channels, yielding stringent limits on contact interactions, extra dimensions, and excited fermions. Overall, the combined LEP and SLD results provide robust SM validation and place tight bounds on new physics scenarios at the TeV scale, guiding future precision electroweak studies.

Abstract

This note presents a combination of published and preliminary electroweak results from the four LEP collaborations and the SLD collaboration which were prepared for the 2001 summer conferences. Averages from Z resonance results are derived for hadronic and leptonic cross sections, the leptonic forward-backward asymmetries, the tau polarisation asymmetries, the b-bbar and c-cbar partial widths and forward-backward asymmetries and the q-qbar charge asymmetry. Above the Z resonance, averages are derived for di-fermion cross sections and forward-backward asymmetries, W-pair, Z-pair and single-W production cross section, electroweak gauge boson couplings, W mass and width and W decay branching ratios. For the first time, total and differential cross sections for di-photon production are combined. The main changes with respect to the experimental results presented in summer 2000 are updates to the Z-pole heavy flavour results from SLD and LEP and to the W mass from LEP. The results are compared with precise electroweak measurements from other experiments. Using a new evaluation of the hadronic vacuum polarisation, the parameters of the Standard Model are evaluated, first using the combined LEP electroweak measurements, and then using the full set of electroweak results.

Figures (9)

• Figure 1: Contours of 68% probability in the $R^0_{\ell}$-$A^{0,\,\ell}_{\mathrm{FB}}$ plane. For better comparison the results for the $\tau$ lepton are corrected to correspond to the massless case. The $\hbox{Standard Model}$ prediction for $m_{\mathrm{Z}}=91.1875$Ge V, $m_{\mathrm{t}}=174.3$Ge V, $m_{\mathrm{H}}=300$Ge V, and $\alpha_{\mathrm{S}}(m_{\mathrm{Z}}^2)=0.118$ is also shown. The lines with arrows correspond to the variation of the $\hbox{Standard Model}$ prediction when $m_{\mathrm{t}}$, $m_{\mathrm{H}}$, $\alpha_{\mathrm{S}}(m_{\mathrm{Z}}^2)$ and $\Delta\alpha_{\mathrm{had}}^{(5)}(m_{\mathrm{Z}}^2)$ are varied in the intervals $m_{\mathrm{t}}=174.3\pm5.1$Ge V, $m_{\mathrm{H}}=300^{+700}_{-186}~\mathrm{ Ge V} \textrm{Ge V}$, $\alpha_{\mathrm{S}}(m_{\mathrm{Z}}^2)=0.118\pm0.002$ and $\Delta\alpha_{\mathrm{had}}^{(5)}(m_{\mathrm{Z}}^2)=0.02761\pm0.00036$, respectively. The arrows point in the direction of increasing values of $m_{\mathrm{t}}$, $m_{\mathrm{H}}$, $\alpha_{\mathrm{S}}$ and $\Delta\alpha_{\mathrm{had}}^{(5)}(m_{\mathrm{Z}}^2)$.
• Figure 2: Measured asymmetries for b and c quark final states as a function of the centre-of-mass energy.
• Figure 3: Contours in the ($R_{\mathrm{b}}^0$,$R_{\mathrm{c}}^0$) plane derived from the LEP+SLD data, corresponding to 68% and 95% confidence levels assuming Gaussian systematic errors. The Standard Model prediction for $m_{\mathrm{t}}=174.3 \pm 5.1$Ge V is also shown. The arrow points in the direction of increasing values of $m_{\mathrm{t}}$.
• Figure 4: Cross-section ratios $r = \sigma_{\rm meas} / \sigma_{\rm QED}$ at different energies. The measurements of the single experiments are displaced by $\pm$ 200 or 400 Me V from the actual energy for clarity. Filled symbols indicate published results, open symbols stand for preliminary numbers. The average over the experiments at each energy is shown as a star. Measurements between 203 and 209 Ge V are averaged to one energy point. The theoretical error is not included in the experimental errors but is represented as the shaded band.
• Figure 5: Examples for angular distributions of the four LEP experiments. Points are the data and the curves are the QED prediction (solid) and the individual fit results for $\Lambda_{\pm}$ (dashed). ALEPH shows the uncorrected number of observed events, the expectation is presented as histogram. For OPAL the histogram represents the number of observed events, before efficiency and radiative corrections are applied.