In addition tott,¯ W+jets and QCD multi-jets, the following components are included as the backgrounds:
• Dibosons (WW,WZ,ZZproductions with additional jets)
• Single top production
• tt+V¯ (V =W,Z)
• Z+jets
They are all estimated by using Monte Carlo with the nominal cross-sections, which are summarized in Table 10. They are not normalized in the Control Regions, thus the uncertainties on cross-section and acceptance into the Signal Regions directly affect the yield estimation. The uncertainties for these backgrounds are discussed in Section 7.2.
Events/50GeV
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1 10 102
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104 ∫Ldt=20.3fb-1, s=8TeV DatatW+jetst
Z+jets QCD Single Top Dibosons
+V t
tWithout Reweighting
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miss
ET
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tWithout Reweighting
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Ldt=20.3fb
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ET
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Z+jets QCD Single Top Dibosons
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Without Reweighting
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miss
ET
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60 80 100 120 140 160
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Figure 54: ETmiss(Left) and mT(Right) distributions of Tight (Top), Loose (middle) and Soft (bottom) Regions. For EmissT plots, the Control Region selections without the upper limit on EmissT is required.
Similarly, formTplot, the Control Regions without the upper limit onmT is applied. The bottom panels show the ratio of data divided by the Monte Carlo. The normalization factors which are determined in the Control Regions are applied here. The error band includes JES uncertainty and statistical uncertainty of Monte Carlo. The magenta line shows the kinematic distributions without the corrections.
7 Uncertainties
7.1 Instrumental uncertainties
The ATLAS detector has been calibrated during two years’ data-taking period, but there still remain inevitable uncertainties in the calibration, such as the uncertainty associating with Jet Energy Scale.
These uncertainties and their impacts on the background estimation are discussed here. Note that the exact impact in the Signal Region is only determined after fitting as discussed in Section 8.1. So here we only show the rough size of impacts. The exact size of the uncertainties will be discussed after fitting.
Instrumental uncertainties are evaluated for all backgrounds and signals.
7.1.1 Jet Energy Scale (JES) uncertainty
As documented in Section 3.2.4, jet calibration is made up of several steps, starting from a single pion calibration toin-situcalibrations. All the nuisance parameters introduced in the calibrations are summed up quadratically and taken into the analysis. Figures 55 show effects of JES uncertainty onmT and the number of jetsNjet40distributions usingt¯tsample. Only minimal kinematic selections are applied in the plots:pTjet1>80 GeV, pTjet3>40 GeV,mT>80 GeV, EmissT >150 GeV, andmeff>500 GeV. The large shift in the entire scale comes form the cumulative impacts of the kinematic selections, which is absorbed after normalizing Monte Carlo in the Control Regions. The remaining shape difference is considered as the uncertainty on transfer factor, which is about 10%.
Events/10GeV
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=8TeV s
-1, Ldt=20.3fb
∫ tt
JES up
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[GeV]
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Ratio
0.8 1 1.2
Events
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=8TeV s
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∫ tt
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JES down
The number of jets
4 6 8 10 12
Ratio 1
1.5
Figure 55: mT(left) and the number of jets (right) comparisons with positive (cyan) and nega-tive (magenta) JES uncertainties. Onlytt¯sample is shown.
7.1.2 Jet Energy Resolution (JER) uncertainty
Uncertainty on jet energy resolution is also considered, which is propagated toETmiss, making an impact in the steep slope after the Jacobian peak inmTas shown in Fig. 56. However, as we set Control Regions close to Signal Regions, overall difference is absorbed by the normalization factors, leaving onlyO(1)%
uncertainty in the final results.
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103
104
=8TeV s
-1, Ldt=20.3fb
∫ tt
JER
[GeV]
mT
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Figure 56:mTcomparison with JER uncertainty. Onlyt¯tsample is shown.
7.1.3 Lepton energy scale, resolution, and trigger/reconstruction efficiency uncertainties
The energy scale and resolution, and also the trigger/reconstruction efficiencies of leptons are calibrated mainly usingZ → llevents. Errors on these calibrations are much smaller compared with JES uncer-tainty, in addition, normalization in the Control Region reduces the uncertainties quite a lot. Even before the normalization, the impacts are as small as 2% in the worst case, so neglected in the fitting.
7.1.4 ETmissresolution uncertainties
The uncertainties of jets and leptons mentioned above are all propagated toEmissT . As shown in Eq. 51, the uncertainty onEmiss (Soft)
T is the last remaining term to be evaluated. Both the energy scale and resolution of the term are varied within the uncertainties, only to find that both of the uncertainties are well below 3%, thus not included in the fitting.
7.1.5 Pile-up uncertainties
The current pile-up simulation does not completely reproduce the number of primary vertex per a colli-sionNPV. Monte Carlo rather predicts 10% lowerNPVthan that of data. We evaluate the impact of this discrepancy by shiftingNPVby±10%. Since our analysis requires a largeETmiss, the impact is only<2%
level, thus not included in the fitting.
7.1.6 b-tagging efficiency uncertainty
b-tagging is used to separateW+jets andt¯t, so the uncertainty directly affects the normalization scales in the Control Regions. b-tagging uncertainty is divided into three components by the flavor of jets: b-, c- and light-jets. The quadrature sum of the uncertainties is taken into the systematic error, which yields about 10% fort¯tin most of the kinematic selections. On the other hand, the uncertainty of mis-tagging is also studied forW+jets, giving a similar size of uncertainty.
7.2 Theoretical uncertainties