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

TL;DR

This note provides a comprehensive, cross-experiment electroweak combination from LEP and SLD, integrating Z-pole precision measurements with LEP-II high-energy results to tightly constrain Standard Model parameters and probe for new physics. It employs a consistent averaging framework (including detailed treatment of correlations and dependencies) and reports both 12- and 14-parameter fits, revealing strong agreement with the SM, a precise estimate of the number of light neutrinos, and stringent limits on contact interactions and other beyond-SM scenarios. The analysis highlights the power of combining diverse electroweak observables—such as Z lineshape, tau polarization, heavy-flavour couplings, and fermion-pair production—to test the SM and guide future explorations. Overall, the results reinforce the SM while providing robust constraints on possible new physics at the TeV scale.

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 2004 summer conferences. [...] The main changes with respect to the experimental results presented in summer 2003 are updates to the W branching fractions and four-fermion cross sections measured at LEP-2, and the SLD/LEP heavy-flavour results measured at the Z pole. The results are compared with precise electroweak measurements from other experiments, notably the final result on the electroweak mixing angle determined in neutrino-nucleon scattering by the NuTeV collaboration, the latest result in atomic parity violation in Caesium, and the measurement of the electroweak mixing angle in Moller scattering. The parameters of the Standard Model are evaluated, first using the combined LEP electroweak measurements, and then using the full set of high-$Q^2$ electroweak results.

Figures (10)

• 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, $m_{\mathrm{t}}=178.0$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 $m_{\mathrm{t}}=178.0\pm4.3$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. The Standard-Model expectations are shown as the lines calculated for $m_{\mathrm{t}}=175~\mathrm{ Ge V} \textrm{Ge V}$ and $m_{\mathrm{H}}=300~\mathrm{ Ge V} \textrm{Ge V}$.
• 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 $m_{\mathrm{t}}=178.0 \pm 4.3$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.