Introduction

We study the prospects of the electroweak fit for two future scenarios:
  • The LHC after the run-2 datataking, with 300 fb-1 of integrated luminosity collected by the ATLAS and CMS experiments
  • The ILC with the GigaZ option
Several improvements in precision for the input measurements and the theoretical uncertainties are expected for these scenarios. For the LHC scenario, the following improvements are considered:
  • The uncertainty on the measurement of MH is assumed to be 100 MeV.
  • A precision of 8 MeV is used for δMW, which is the uncertainty of the W-boson mass measurement.
  • An experimental uncertainty of 0.5 GeV is used for the mass of the top quark mt. The theoretical uncertainty due to the conversion to the MSbar mass is taken to be 0.25 GeV.
For the ILC/GigaZ scenario the following benchmark uncertainties are used:
  • The uncertainty on the measurement of MW is assumed to be 5 MeV.
  • An experimental uncertainty of 30 MeV is used for the mass of the top quark mt, with a theoretical uncertainty of 100 MeV.
  • The uncertainty on the measurement of the effective weak mixing angle sin2θleff is taken to be 1.3·10-5.
  • The partial decay width of the Z boson to leptons, R0l, is assumed to be measured to a precision of 4·10-3.
For both scenarios, common improvements are assumed on the precision of the hadronic vacuum polarization Δαhad(5)(MZ2) and theory predictions:
  • The uncertainty on the measurement of Δαhad(5)(MZ2) is taken to be 4.7·10-5.
  • The theoretical uncertainties are reduced by a factor of four, implying the availability of electroweak three-loop and mixed electroweak/QCD higher order corrections.
The impact of these improvements on the electroweak fit are studied using a fit setup with a reduced set of parameters. The set of parameters is MH, MW, MZ, mt, sin2θleff, Δαhad(5)(MZ2) and R0l. The central values of the measurements are adjusted to give a fully consistent set of SM observables.
More information on the fit setup and the expected improvements can be found in our latest publication.

Prospects for the electroweak fit in the SM

The following figures show the expected improvements in precision for the prediction of SM observables from the electroweak fit. These are compared to the present status of the electroweak fit, but with the same reduced set of input variables as described above.

Δχ2 as a function of Higgs boson mass MH. The solid and dashed lines give the results when including and ignoring theoretical errors, respectively. The dark blue band shows the present result from the SM fit, while the light blue shows the fit with the reduced input and adjusted central values to obtain MH=125 GeV. The LHC scenario is shown in green, and ILC scenario is shown in orange.
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Δχ2 as a function of W boson mass MW. The solid and dashed lines give the results when including and ignoring theoretical errors, respectively. The dark blue band shows the result from the SM fit with the present uncertainties. The LHC scenario is shown in green, and ILC scenario is shown in orange. The measurement point is drawn with the present uncertainty and the prospects for the LHC and ILC measurements.
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Δχ2 as a function of the effective weak mixing angle sin2θleff. The solid and dashed lines give the results when including and ignoring theoretical errors, respectively. The dark blue band shows the result from the SM fit with the present uncertainties. The LHC scenario is shown in green, and ILC scenario is shown in orange. The measurement point is drawn with the present uncertainty and the prospects for the LHC and ILC measurements.
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Contours of 68% and 95% confidence level obtained from scans of fits with fixed variable pairs MW vs. mt. The precision obtained from the present fit (blue) is compared with the LHC (green) and ILC/GigaZ (orange) scenarios. The horizontal bands indicate the 1σ regions of the MW and mt measurements (world averages) with today's and the prospective LHC and ILC precision.
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Contours of 68% and 95% confidence level obtained from scans of fits with fixed variable pairs MW vs. sin2θeff. The precision obtained from the present fit (blue) is compared with the LHC (green) and ILC/GigaZ (orange) scenarios. The horizontal bands indicate the 1σ regions of the MW and sin2θeff measurements (world averages) with today's and the prospective LHC and ILC precision.
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Prospects for the Oblique Parameters

The constraints on the STU parameters are derived from a fit using the setup described above. The following fit results are determined from a fit for a reference Standard Model with mt,ref=173 GeV and MH,ref=125 GeV.

More details can also be found in the Oblique Parameters section. Due to the reduced parameter set, only S and T are determined with the U parameter fixed to zero. Because of the fully consistent set of SM input parameters, the central values for the S and T parameters are zero. The precision for the present scenario are:

δS = 0.098
δT = 0.086
with correlation coefficient 0.93.

The expected precision for the LHC scenario are:

δS = 0.086
δT = 0.064
with correlation coefficient 0.96.

The expected precision for the ILC scenario are:

δS = 0.018
δT = 0.023
with correlation coefficient 0.91.

Contours of 68% and 95% confidence level in the TS-plane, where U was constrained to 0 in the fit. The reference point at which all oblique parameters vanish is defined by MH=125 GeV and mt=173 GeV.
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Prospects for Higgs Couplings

Modified Higgs couplings are tested in an effective theory approach, where all bosons and all fermion couplings are modified in the same way, scaled by the variables κV and κF, respectively. In the SM, κV = κF = 1. More details about this model can be found in the Higgs Couplings section.

Contours of 68% and 95% confidence level in the MW vs. κV plane. The precision obtained from the present fit (blue) is compared with the LHC (green) and ILC/GigaZ (orange) scenarios. The horizontal bands indicate the 1σ regions of the direct MW and κV measurements with today's and the prospective LHC and ILC precision.
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