Precision Electroweak Measurements and Constraints on the Standard Model

TL;DR

This work compiles precision electroweak measurements from LEP, SLD, and Tevatron to perform global Standard Model fits and constrain fundamental parameters such as m_Z, m_t, m_W, m_H, α_S(m_Z^2), and Δα^(5)_had(mZ^2). By combining high-Q^2 data (Z-pole observables, W boson properties, and top-quark mass) with selected low-Q^2 measurements, the analysis tests SM consistency and derives indirect constraints on the Higgs mass, generally favoring a light Higgs while acknowledging uncertainties from hadronic vacuum polarization and higher-order corrections. The results show good agreement between indirect and direct measurements of m_W and m_t, with Higgs-mass constraints indicating a relatively low mh, and the inclusion of direct Higgs searches elevating the upper limit. The study highlights the importance of precise α(m_Z^2) and outlines future prospects for tighter constraints with continued data from Tevatron and LHC, as well as ongoing theoretical refinements in electroweak corrections.

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 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 2008 are new combinations of results on the W-boson mass 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 if among the electroweak radiative corrections only the photon vacuum polarisation is included. The associated 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 in the region favoured by theory ($<1000~\mathrm{Ge V}$) and allowed by direct searches ($114~\mathrm{Ge V}$ to $170~\mathrm{Ge V}$ and $>180~\mathrm{Ge V}$). The arrow labelled $\Delta\alpha$ shows the variation of this relation if $\alpha(m_{\mathrm{Z}}^2)$ is changed by plus/minus 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 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 ($160~\mathrm{Ge V}$ to $170~\mathrm{Ge V}$).
• 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 searches at LEP-II (up to $114~\mathrm{Ge V}$) and the Tevatron ($160~\mathrm{Ge V}$ to $170~\mathrm{Ge V}$).
• 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 ($160~\mathrm{Ge V}$ to $170~\mathrm{Ge V}$). 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.