Precision Electroweak Measurements and Constraints on the Standard Model

TL;DR

This work compiles and analyzes precision electroweak measurements from LEP, SLC, and the Tevatron to test the Standard Model and constrain its parameters. By combining high-$Q^2$ data (Z-pole observables, $m_W$, $\Gamma_W$, $m_t$) with selected low-$Q^2$ inputs (APV, Møller, NuTeV), the authors perform global SM fits using $\Delta\alpha^{(5)}_{\mathrm{had}}(m_Z^2)$, $\alpha_S(m_Z^2)$, $m_Z$, $m_t$, and $\log_{10}(m_H)$ as free parameters. The results generally agree with SM predictions and favor a relatively light Higgs boson, placing a 95% CL upper limit near 150–160 GeV, while indirect constraints on $m_W$ and $m_t$ align with direct measurements; a notable NuTeV anomaly in neutrino-nucleon scattering challenges the completeness of the fit. The analysis highlights the importance of precise hadronic vacuum polarization inputs and higher-order corrections in shaping Higgs-related inferences. These precision tests provide a powerful indirect framework for validating the SM before direct Higgs discoveries and guide future experimental priorities.

Abstract

This note presents constraints on Standard Model parameters using published and preliminary precision electroweak results measured at the electron-positron colliders LEP and SLC. The results are compared with precise electroweak measurements from other experiments, notably CDF and DØat the Tevatron. Constraints on the input parameters of the Standard Model are derived from the 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 2007 are new combinations of results on the W-boson mass and width 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 shows the predictions if among the electroweak radiative corrections only the photon vacuum polarisation is included. The corresponding arrow shows variation of 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. The arrow labelled $\Delta\alpha$ shows the variation of this relation if $\alpha(m_{\mathrm{Z}}^2)$ is changed by one 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 data except the direct measurement of $m_{\mathrm{W}}$, 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 search.
• Figure 4: The 68% confidence level contour in $m_{\mathrm{t}}$ and $m_{\mathrm{H}}$ for the fit to all 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 search.
• 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 search. 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.