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 publicationUpdate of the global electroweak fit and constraints on two-Higgs-doublet models .
Theoretical predictions
For the following results the latest theoretical predictions of electroweak observables are used. In particular:
- The mass of the W boson (MW) is calculated with the full two-loop corrections and known beyond-two-loop corrections from
(M. Awramik et al., Phys. Rev. D69, 053006 (2004), hep-ph/0311148). We use the latest update from 2014, which includes the known four-loop QCD correction to the rho parameter and a more recent value of the Fermi constant. - The effective weak mixing angle (sin2θeffl) is calculated with the full two-loop corrections and known beyond-two-loop corrections from
(M. Awramik et al., JHEP 0611, 048 (2006), hep-ph/0608099)
(M. Awramik et al., Nucl. Phys. B813, 174 (2009), arXiv:0811.1364), and
(I. Dubovyk et al., Phys. Lett. B762, 184 (2016), arXiv:1607.08375) - The partial and total widths of the Z and the hadronic peak cross section are calculated with the EW two-loop corrections and known beyond-two-loop corrections from
(A. Freitas, JHEP 1404, 070 (2014), hep-ph/1401.2447). - The total width of the W boson makes use of the parametrizations of ((Cho et. al, JHEP 1111, 068 (2011), arXiv:1104.1769, see also older papers 1, 2, 3).
- The determination of the strong coupling makes use of the complete fourth-order (3NLO) calculation of the hadronic Z width (P. A. Baikov et al., Phys. Rev. Lett. 108, 222003 (2012), arXiv:1201.5804) .
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 =18.6 for 15 degrees of freedom, giving the p-value Prob(χ2min,15)=0.23.| 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 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. In the fifth column the fit results are given without using the corresponding experimental or phenomenological estimate in the given row. The last column shows the results ignoring all theoretical uncertainties. |
.eps
|
| 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. |
.eps
|
| 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. |
.eps
|
| Determination of MH excluding all the sensitive observables from the fit, except for the one given. |
.eps
|
| 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. |
.eps
|
| 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. |
.eps
|
| 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 direct measurements of MW are indicated by dots with 1σ error bars. |
.eps
|
| 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 average of the LEP and SLD measurements of sin2θeff is indicated by a red dot with 1σ error bars; the Tevatron combination is shown as a black dot. |
.eps
|
| Δχ2 versus the hadronic contribution to the vacuum polarisation, shown as blue band. Also shown is the result of the fit without the MH measurement (grey band). A recent estimation of Δαhad(MZ2) is shown as red dot with 1σ error bars. |
.eps
|
| Δχ2 versus the running strong coupling at MZ, shown as blue band. The grey lines show results where only measurements of ΓZ, R0l and σ0had 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. |
.eps
|
| 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 measurement, respectively. The horizontal bands indicate the 1σ regions of the MW and mt measurements. |
.eps
|
| Contours of 68% and 95% confidence level obtained from scans of fits with fixed variable pairs MW vs. sin2θeff. 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 sin2θeff measurements (world averages). |
.eps
|
