The global electroweak fit at NNLO and prospects for the LHC and ILC

TL;DR

Baak et al. update the global electroweak fit to NNLO theory, incorporating full fermionic two-loop Z widths and four-loop QCD corrections to M_W, and assess the impact of theoretical uncertainties. The analysis finds SM consistency with current data (χ2_min=17.8/14) and yields improved indirect determinations for M_W and sin^2θ_eff, as well as tightened oblique parameter constraints (S,T,U). They project the prospects of Phase-1 LHC and ILC/GigaZ, showing that ILC/GigaZ can deliver major gains in indirect precision for MW, sin^2θ_eff, M_Z, and Δα_had, provided theoretical uncertainties are reduced accordingly. The paper also analyzes Higgs coupling modifications in a κ_V, κ_F framework, finding that including EW observables strengthens constraints on κ_V beyond Higgs data alone, while κ_F constraints are less affected. Overall, precision EW fits remain a powerful probe of SM consistency and indirect new-physics scales at future colliders.

Abstract

For a long time, global fits of the electroweak sector of the Standard Model (SM) have been used to exploit measurements of electroweak precision observables at lepton colliders (LEP, SLC), together with measurements at hadron colliders (Tevatron, LHC), and accurate theoretical predictions at multi-loop level, to constrain free parameters of the SM, such as the Higgs and top masses. Today, all fundamental SM parameters entering these fits are experimentally determined, including information on the Higgs couplings, and the global fits are used as powerful tools to assess the validity of the theory and to constrain scenarios for new physics. Future measurements at the Large Hadron Collider (LHC) and the International Linear Collider (ILC) promise to improve the experimental precision of key observables used in the fits. This paper presents updated electroweak fit results using newest NNLO theoretical predictions, and prospects for the LHC and ILC. The impact of experimental and theoretical uncertainties is analysed in detail. We compare constraints from the electroweak fit on the Higgs couplings with direct LHC measurements, and examine present and future prospects of these constraints using a model with modified couplings of the Higgs boson to fermions and bosons.

Figures (9)

• Figure 1: Left: Comparison of the fit results with the direct measurements in units of the experimental uncertainty. The fit results are compared between the scenario using the two-loop calculations of the $Z$ partial widths with the four-loop $\mathcal{O}(\alpha_t \alpha_s^3)$ correction to $M_W$ (colour, top bars), and the one-loop calculation used in a previous publication Baak:2011ze (shaded gray, bottom bars). Right: Comparison of the fit results with the indirect determination in units of the total uncertainty, defined as the uncertainty of the direct measurement and that of the indirect determination added in quadrature. The indirect determination of an observable corresponds to a fit without using the corresponding direct constraint from the measurement.
• Figure 2: Contours at 68% and 95% CL obtained from scans of $M_W$ versus $m_t$ (top) and $M_W$ versus $\sin\!^2\theta^{\ell}_{{\rm eff}}\xspace$ (bottom), for the fit including $M_{H}$ (blue) and excluding $M_{H}$ (grey), as compared to the direct measurements (vertical and horizontal green bands and ellipses). The theoretical uncertainty of 0.5 GeV is added to the direct top mass measurement. In both figures, the corresponding direct measurements are excluded from the fit. In the case of $\sin\!^2\theta^{\ell}_{{\rm eff}}\xspace$, all partial and full $Z$ width measurements are excluded as well (except in case of the orange prediction), besides the asymmetry measurements.
• Figure 3: Contours at 95% CL obtained from scans of $M_W$ versus $\sin\!^2\theta^{\ell}_{{\rm eff}}\xspace$, with the top mass theoretical uncertainty varied between 0 and 1.5 $\mathrm{Ge V}$ in steps of 0.5 $\mathrm{Ge V}$, as compared to the direct measurements (vertical and horizontal green bands). The corresponding direct measurements are excluded from the fit.
• Figure 4: Constraints on the oblique parameters $S$ and $T$, with the $U$ parameter fixed to zero, using all observables (blue). Individual constraints are shown from the asymmetry measurements (yellow), the Z partial and total widths (green) and $W$ mass and width (red), with confidence levels drawn for one degree of freedom. The SM prediction within uncertainties is indicated by the thin black stroke.
• Figure 5: Profiles of $\Delta\chi^2\xspace$ versus $M_H$ (top), $M_W$ (middle) and $\sin\!^2\theta^{\ell}_{{\rm eff}}\xspace$ (bottom). In blue the present result, and in light blue, green and orange the present, LHC and ILC/GigaZ scenarios, respectively, all using the future fit setup (reproducing $M_H\simeq125\;$GeV) with corresponding uncertainties. The impact of the theoretical uncertainties is illustrated by the width of the coloured curves. See Table \ref{['tab:results_best']} for the numerical results of these fits.