Introduction

The global fit to electroweak precision data routinely performed by the LEP electroweak working group and others, demonstrates impressively the predictive power of electroweak unification and quantum loop corrections. We have performed the fit using the most recent experimental measurements and state-of-the-art SM predictions.

Note: We interpret the new boson discovered at the LHC as the SM Higgs boson and use the measurements from ATLAS and CMS for the Higgs boson mass MH. More details can be found in our latest publication The Electroweak Fit of the Standard Model after the Discovery of a New Boson at the LHC.

New since the last publication:

  • Changed Rb calculation following the publication JHEP 1208 (2012) 050 and Erratum-ibid. 1305 (2013) 074, see also [arXiv:1205.0299].
  • New top mass measurement by the Tevatron experiments [arXiv:1305.3929]

Theoretical predictions

For the following results the latest theoretical predictions of electroweak observables are used. In particular:


Fit results of the current global fit

In the following tables and figures the experimental input used in the fit and the fit results are given. All fits discussed here minimise the test statistics χ2 which accounts for the deviations between the observables given in the table below and their SM predictions. The fit converges at the global minimum value χ2min =18.1 for 14 degrees of freedom, giving the naive p-value Prob(χ2min,14)=0.20. Excluding the experimental information on MH the fit converges at the global minimum value χ2min =16.7 for 13 degrees of freedom, giving a naive p-value of Prob(χ2min,13)=0.21. See the Section Probing the SM for a more accurate toy-MC-based determination of the p-value.

With the measurement of MH it is for the first time possible to fully predict all Standard model parameters / observables with only a minimal set of input parameters. The minimal set of parameters needed are MH together with all fermion masses, αs(MZ2) and three parameters defining the electroweak sector and its radiative corrections, here chosen to be MZ, GF and Δαhad(MZ2). The prediction based on these sets of parameters is shown in some figures below where it is called "SM fit with minimal input".

Table: Input values and fit results for the observables and parameters of the global electroweak fit. The first and second columns list respectively the observables/parameters used in the fit, and their experimental values or phenomenological estimates. The subscript ``theo'' labels theoretical error ranges. The third column indicates whether a parameter is floating in the fit. The fourth column quotes the results of the complete fit including all experimental data. The fifth column gives the fit results for each parameter without using the MH measurement in the fit. In the last column the fit results are given without using the corresponding experimental or phenomenological estimate in the given row.
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Comparing fit results with direct measurements: pull values for the SM fit, i.e. deviations between experimental measurements and theoretical calculations in units of the experimental uncertainty.
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Comparing fit results with direct measurements: pull values for the SM fit with and without inclusion of MH in the fit. The pull values are defined as deviations between experimental measurements and theoretical calculations in units of the experimental uncertainty.
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Comparing fit results (orange bars) with indirect determinations (blue bars) and direct measurements (data points): pull values for the SM fit defined as deviations to the indirect determinations. The total error is taken to be the error of the direct measurement added in quadrature with the error from the indirect determination. This plot is a graphical representation of the numbers presented in the above table.
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Determination of MH excluding all the sensitive observables from the fit, except for the one given.

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Δχ2 as a function of Higgs boson mass MH, shown as blue band. Also shown is the result of the fit without the MH measurements (grey band). The solid and dashed lines give the results when including and ignoring theoretical errors, respectively.
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Δχ2 as function of the top mass mt, shown as blue band. Also shown is the result of the fit without the MH measurements (grey band). In both cases the direct determinations of mt were excluded from the fit. Direct determinations of mt are indicated by dots with 1σ error bars.
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Δχ2 versus MW, shown as blue band. Also shown is the result of the fit without the MH measurements (grey band). In both cases the direct measurements of MW were excluded from the fit. The Standard Model fit with minimal input (see above) is shown as a black line. The experimental world average of MW is indicated by a dot with 1σ error bars.
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Δχ2 versus the effective weak mixing, shown as blue band. Also shown is the result of the fit without the MH measurement (grey band). In both cases all precision observables sensitive to sin2θeff are excluded from the fit. The Standard Model fit with minimal input (see above) is shown as a black line. The average of the LEP and SLD measurements of sin2θeff is indicated by a dot with 1σ error bars.
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Δχ2 versus the running strong coupling at MZ, shown as blue band. The green band shows the Standard Model fit with minimal input, where the value of αS(MZ2) is left free in the fit and instead measurements of σ0had and R0l are used as input parameters. The value of αS(MZ2) determined from τ decays at N3LO is indicated by a dot with 1σ error bars.
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Contours of 68% and 95% confidence level obtained from scans of fits with fixed variable pairs MW vs. mt. The narrower blue and larger grey allowed regions are the results of the fit including and excluding the MH measurements, respectively. The horizontal bands indicate the 1σ regions of the MW and mt measurements (world averages).
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Probing the Standard Model

We evaluate the p-value of the global SM fit using a toy MC simulation with 20000 experiments. These are generated using as true values for the SM parameters the outcomes of the global fit. For each toy simulation, the central values of all of the observables used in the fit are generated according to Gaussian distributions around their expected SM values (given the parameter settings) with standard deviations equal to the full experimental errors taking into account all correlations. Fair agreement is observed between the empirical toy MC distribution and the χ2 function expected for Gaussian observables.

Result of the MC toy analysis of the SM fit. Shown are the χ2min distribution of a toy MC simulation (open histogram), the corresponding distribution for a fit ignoring theoretical errors (shaded/green histogram), an ideal χ2 distribution assuming a Gaussian case with ndof=14 (black line) and the p-value as a function of the χ2min of the global fit.
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