Precision Electroweak Measurements and Constraints on the Standard Model

TL;DR

The paper compiles and analyzes precision electroweak measurements from LEP, SLC, and the Tevatron, combining Z-pole observables, W-boson properties, top-quark mass, and selected low-$Q^2$ measurements to perform global Standard Model fits. It uses these fits to constrain SM parameters such as $m_t$, $m_H$, $ riangleoldsymbol{ extalpha}^{(5)}_{ ext{had}}(m_Z^2)$, and $oldsymbol{ extalpha_s(m_Z^2)}$, highlighting the strong sensitivity to $m_t$ and the logarithmic sensitivity to $m_H$ through loop corrections. The results largely support the SM while favoring a relatively light Higgs boson region, with precise $m_W$ measurements and hadronic vacuum polarization uncertainties playing key roles; notable tensions arise from the NuTeV result and LEP/SLC leptonic mixing-angle spread. The authors discuss theoretical uncertainties, methodological approaches (MINUIT, ZFITTER), and future prospects, including improved measurements at LEP-II, Tevatron Run II, and the LHC. Overall, the work provides a comprehensive, high-precision test of the SM at high energies and delineates the path toward tighter Higgs-sector and electroweak parameter constraints.

Abstract

This note presents constraints on Standard Model parameters using published and preliminary precision electroweak results obtained at the electron-positron colliders LEP and SLC. The results are compared with precise electroweak measurements from other experiments, notably CDF and DØ at the Tevatron. Constraints on the input parameters of the Standard Model are derived from the combined set of results obtained in high-$Q^2$ interactions, and used to predict results in low-$Q^2$ experiments, such as atomic parity violation, Møller scattering, and neutrino-nucleon scattering. The main changes with respect to the experimental results presented in 2009 are new combinations of results on the width of the W boson and the mass of the top quark.

Figures (6)

• Figure 1: $\mathrm{\hbox{LEP-I}}$+SLD measurements bib-Z-pole of $\sin^2\theta_{\mathrm{eff}}^{\mathrm{lept}}$ and $\Gamma_{\ell\ell}$ and the SM prediction. The point with the arrow labelled $\Delta\alpha$ shows the prediction when only the photon vacuum polarisation is included in the electroweak radiative corrections. The associated arrow shows the variation in this prediction if $\alpha(m_{\mathrm{Z}}^2)$ is changed by one standard deviation. This variation gives an additional uncertainty to the SM prediction shown in the figure.
• Figure 2: The comparison of the indirect constraints on $m_{\mathrm{W}}$ and $m_{\mathrm{t}}$ based on $\mathrm{\hbox{LEP-I}}$/SLD data (dashed contour) and the direct measurements from the $\mathrm{\hbox{LEP-II}}$/Tevatron experiments (solid contour). In both cases the 68% CL contours are plotted. Also shown is the SM relationship for the masses as a function of the Higgs mass in the region favoured by theory ($<1000~\mathrm{Ge V}$) and not excluded by direct searches ($114~\mathrm{Ge V}$ to $158~\mathrm{Ge V}$ and $>175~\mathrm{Ge V}$). The arrow labelled $\Delta\alpha$ shows the variation of this relation if $\alpha(m_{\mathrm{Z}}^2)$ is varied between $-1$ and $+1$ standard deviation. This variation gives an additional uncertainty to the SM band shown in the figure.
• Figure 3: The 68% confidence level contour in $m_{\mathrm{W}}$ and $m_{\mathrm{H}}$ for the fit to all high-$Q^2$ data except the direct measurement of $m_{\mathrm{W}}$, indicated by the shaded horizontal band of $\pm1$ sigma width. The vertical bands shows the 95% CL exclusion limit on $m_{\mathrm{H}}$ from the direct searches at LEP-II (up to $114~\mathrm{Ge V}$) and the Tevatron ($158~\mathrm{Ge V}$ to $175~\mathrm{Ge V}$).
• Figure 4: The 68% confidence level contour in $m_{\mathrm{t}}$ and $m_{\mathrm{H}}$ for the fit to all high-$Q^2$ data except the direct measurement of $m_{\mathrm{t}}$, indicated by the shaded horizontal band of $\pm1$ sigma width. The vertical band shows the 95% CL exclusion limit on $m_{\mathrm{H}}$ from the direct searches at LEP-II (up to $114~\mathrm{Ge V}$) and the Tevatron ($158~\mathrm{Ge V}$ to $175~\mathrm{Ge V}$).
• Figure 5: $\Delta\chi^{2}=\chi^2-\chi^2_{min}$vs.$m_{\mathrm{H}}$ curve. The line is the result of the fit using all high-$Q^2$ data (last column of Table \ref{['tab-BIGFIT']}); the band represents an estimate of the theoretical error due to missing higher order corrections. The vertical band shows the 95% CL exclusion limit on $m_{\mathrm{H}}$ from the direct searches at LEP-II (up to $114~\mathrm{Ge V}$) and the Tevatron ($158~\mathrm{Ge V}$ to $175~\mathrm{Ge V}$). The dashed curve is the result obtained using the evaluation of $\Delta\alpha^{(5)}_{\mathrm{had}}(m_{\mathrm{Z}}^2)$ from Reference bib-Troconiz-Yndurain-2004. The dotted curve corresponds to a fit including also the low-$Q^2$ data from Table \ref{['tab-SMpred']}.