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

TL;DR

This comprehensive combination synthesizes LEP and SLD electroweak measurements across Z-pole and LEP-II energies to constrain Standard Model parameters. By performing global fits to Z lineshape, leptonic and heavy-flavor observables, and high-energy fermion-pair and photon-pair processes, the study tests lepton universality, determines the number of light neutrinos, and places limits on new physics scenarios. The results show overall agreement with SM predictions, with precise determinations of m_Z, Gamma_Z, R_b^0, R_c^0, and couplings, while providing stringent limits on contact interactions, extra dimensions, excited leptons, and other beyond-SM effects. Together, these measurements sharpen indirect constraints on the Higgs sector and gauge couplings, informing future collider expectations and global electroweak fits.

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 2003 summer conferences. Averages from $\Zzero$ resonance results are derived for hadronic and leptonic cross sections, the leptonic forward-backward asymmetries, the $τ$ polarisation asymmetries, the $\bb$ and $\cc$ partial widths and forward-backward asymmetries and the $\qq$ charge asymmetry. Above the $\Zzero$ resonance, averages are derived for di-fermion cross sections and forward-backward asymmetries, photon-pair, W-pair, Z-pair, single-W and single-Z cross sections, electroweak gauge boson couplings, W mass and width and W decay branching ratios. Also, an investigation of the interference of photon and Z-boson exchange is presented, and colour reconnection and Bose-Einstein correlation analyses in W-pair production are combined. The main changes with respect to the experimental results presented in summer 2002 are updates to the mass of the W boson, four-fermion cross sections and gauge couplings, all measured at LEP-2, and the LEP heavy-flavour results measured at the Z pole. The results are compared with precise electroweak measurements from other experiments, notably the recent final result on the electroweak mixing angle determined in neutrino-nucleon scattering by the NuTeV collaboration and the new result in atomic parity violation in Caesium. 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 (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, $m_{\mathrm{t}}=174.3$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. 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 $m_{\mathrm{t}}=174.3 \pm 5.1$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.