All sources of systematic uncertainties as described in section 5.6 are expected to have an influence on the measured top quark pair production cross section. All uncertainties that can be considered as continuous are included as nuisance parameters in the profile likelihood fit function Lβδ. Sources of systematic uncertainties representing discrete settings, for example the difference between the two event generators MC@NLO and POWHEG, are evaluated using pseudo-experiments. A summary of the systematic uncertainties considered in this analysis is shown in table 6.4, also indicating which ones are treated as nuisance parameters in the fit.
The influence of different uncertainties on the predicted number of events and the likelihood discrimi-nantD can be seen in figure ??for theµ+jets channel and figure 6.10 for thee+jets channel. Total systematic modeling and detector uncertainties are shown separately, and are constructed from the different template distributions assuming full correlation of uncertainties across the different physics processes and no correlation between the different sources of uncertainties. The model uncertain-ties also include the uncertainuncertain-ties on the predictions for the different background processes, which are implemented as Gaussian constraints on the corresponding normalization parameters βi in the likelihood.
The uncertainties can act on the shape of the distribution, the overall number of predicted events, the ratio of events with different jet multiplicities or all together. As an example, the b- and mistag calibration uncertainties cannot change the number of predicted events, but can only lead to differences in the shapes of D for various physics processes. As expected, the b-tag uncertainties have a significant influence on the shape of the discriminant D for t¯t events, and to a much smaller extend on the W+jets backgrounds, while the picture is inverted for the uncertainties on the mistag calibration. This behavior can be seen in figure ??, showing the ratio of default and ±1σ varied distributions at the 50% efficiency JetProb working point in µ+4 jets events for t¯t and W+jets processes. Since the discriminant for t¯t events in the µ+4 jets channel peaks at a value of D = 1, and at D = 0 for W + jets, the variation in the corresponding outermost bins has the largest influence on the measurement, and there the behavior as described above is visible.
On the other hand, many systematic uncertainties have a large influence on the ratio of events predicted at the different jet multiplicities. This is especially true for jet related uncertainties or theoretical models predicting a different amount of additional radiation in the events, as can be seen in figure 6.11. The final combined fit to extract the signal cross section, σt¯t, makes use of both shape uncertainties and differences in the jet multiplicity distribution. Therefore, the classification of events with njets = 3,4, ≥ 5 improves the performance of the method over the same method applied to a njets ≥3 selection of events.
Systematic Uncertainty Nuisance Parameter Comments
Background Normalization - included in statistical uncertainty through Gaussian constrains
Signal Generator
-Parton Shower Model
-ISR and FSR - ISR±, FSR±, ISRFSR± - largest
dif-ference taken as symmetric uncer-tainty
-W+Jets Generator Settings - reweighting for iqopt2 and ptjmin10 W+Heavy Flavor Contribution X six different parameters: W b¯b/W c¯c
and W c separately for njets = 3,4, ≥ QCD Multijet Model - 5from anti-electron (e+jets) and
loose-not-tight (µ+jets) selection
Pile-Up Model X
Monte Carlo Statistics
-Muon/Electron Scale Factors X uncorrelated between the channels Muon Momentum Scale and
Resolution X one combined parameter for the
enve-Electron Energy Scale X lope
Electron Energy Resolution X
Calorimeter Response (JES) X
η-Intercalibration (JES) X
Noise Term (JES) X
Parton Shower Model (JES) X
Underlying Event Model (JES) X
Pile-Up Influence on JES X
Close-By Jets (JES) X
Flavor Composition (JES) X flavor composition fromt¯tMC for sig-nal, 50:50 quark/gluon contribution for all backgrounds
b-Jet Energy Scale X
Jet Energy Resolution X
Jet Reconstruction Efficiency X
ETmiss Uncertainties X fully correlated uncertainties on soft jet and cell out terms
b-Tagging Calibration X one δ for each of the four working points
Mistagging Calibration X one δ for each of the four working
points
Table 6.4.: Sources of systematic uncertainties and their treatment in the cross section extraction.
The first set of uncertainties is related to assumptions on the physics model, while the second set is related to detector and reconstruction effects.
Likelihood Discriminant
Figure 6.14.: Sum of all sources of systematic uncertainties (yellow band) for physics modeling uncertainties (left) and detector uncertainties (right) for the sum of predicted signal and background, compared to data in theµ+jets channel.
Likelihood Discriminant
Figure 6.15.: Sum of all sources of systematic uncertainties (yellow band) for physics modeling uncertainties (left) and detector uncertainties (right) for the sum of predicted signal and background, compared to data in thee+jets channel.
Likelihood Discriminant
(a) b-Tagging calibration uncertainty on the 50% efficiencyJetProbworking point.
Likelihood Discriminant
(b) Mistag calibration uncertainty on the 50% efficiencyJetProbworking point.
Figure 6.16.: Shape changes of the likelihood discriminantD caused by theb-tag and mistag cali-bration uncertainties at the 50% efficiency working point, and their difference between t¯t and W+jets events.
Analysis Channel
(a) Calorimeter Response Jet Energy Scale Uncer-tainty
(b) Flavor Composition Jet Energy Scale Uncertainty
Analysis Channel
(c) Final State Radiation Uncertainty
Analysis Channel
(d) Signal Generator (POWHEG vs MC@NLO sym-metrized)
Figure 6.17.: Distribution of all selected simulated t¯t events in the different analysis channels and the sensitivity of the relative amount of events in each channel on different sources of systematic uncertainties.