Thee/γ backgrounds and the systematic uncertainties have been also determined as a function of the photon transverse energy. Therefore, an extraction of theσttγ¯ differentially is also possible.
Nine exclusiveET(γ)bins have been selected. Because theET(γ)spectrum decreases exponen-tially the bins are increasingly coarser. The measurement stops for photons withET(γ)>300 GeV for which un upper limit at 95% Confidence Level (CL) on thet¯tγ final state is derived.
The same procedure, used for deriving the inclusive cross section, has been applied in each ET(γ) bin, extracting the σt¯tγ by minimising the likelihood ratio of Eq. 5.34.
The number of signal and background events extracted form the likelihood fit in each ET(γ) bin are shown in Fig. 8.8. It can be seen that the total number of events (signal plus backgrounds) is in good agreement with the number of candidate events. Because of the small size of data some fluctuations are present, but overall the fluctuations are within one gaussian standard deviation.
Events / GeV
10-2
10-1
1 10
102 Electron channel
Data
102 Muon channel
Data
Figure 8.8: Number of signal and background events as extracted from the likelihood fit and as a function of the photon transverse energy. Results are projected to the electron (left) and muon (right) channels respectively. The number of candidate events is shown with filled markers. The white histogram indicates the number of signal events. The filled histograms show the number of hadron fakes and the number of e/γ background events respectively. The uncertainties on the number of signal events are shown with two bands. The dashed band corresponds to the stat⊕uncertainty, while the hatched band corresponds to the statistical uncertainty. The bottom plot in each figure shows the normalised residuals (Pull) of the total number of events extracted from the fit to the number of data candidates. The filled area corresponds to the inclusion of systematic uncertainties in the calculation of the residuals.
The extracted t¯tγ cross sections are summarised in Tab. 8.5. The systematic component of the uncertainty is comparable to the statistical component for the firstET(γ) bins, however, the measurement is rapidly dominated by the statistical uncertainty.
The addition of the σt¯tγ measurements in all ET(γ) bins gives a value of 66 fb which is close to that obtained in Eq. 8.2.
ET(γ) range [GeV] σt¯tγ [fb]
]20,30[ 30.56 +6.36−6.18(stat)+5.94−4.78(syst) [30,40[ 10.10 +4.01−3.68(stat)+2.50−1.95(syst) [40,50[ 9.35 +2.90−2.66(stat)+2.14−1.78(syst) [50,70[ 9.35 +2.60−2.36(stat)+1.82−1.26(syst) [70,120[ 3.63 +2.46−2.27(stat)+1.38−1.06(syst) [120,180[ 1.91 +1.42−1.21(stat)+0.58−0.38(syst) [180,250[ 0.97 +0.63−0.53(stat)+0.32−0.23(syst) [250,300[ 0.40 +0.52−0.33(stat)+0.21−0.15(syst) [300,∞) <1.45 fb at 95% CL Total 66.3+9.1−8.5(stat)
Table 8.5: Summary ofσt¯tγ as a function of ET(γ). The entry labelled by “Total” corresponds to the sum of all components, statistical have ben added quadratically.
8.4.1 Uncertainties
The determination of the relative strength of each component of the systematic uncertainty to the cross section was evaluated using the same method as for the inclusive measurement. The full breakdown is presented in Tab. 8.6, while a a condensed version is shown in Fig. 8.9.
The low-ET(γ) range (20→50 GeV) is dominated by the uncertainty on parton shower mod-elling (0.65 %/GeV), on the signal template modmod-elling (0.60%/GeV), on the photon identification (0.41%/GeV) and on the modelling of the QED radiation (0.40%/GeV). The same uncertainties remain important with increasing ET(γ), however the uncertainty on e→ γ increases its contri-bution to the total.
Results 164
Component ET(γ) range [GeV]
]20,30[ [30,40[ [40,50[ [50,70[ [70,120[ [120,180[ [180,250[ [250,300[
Signal modelling [%/GeV]
MC generator 0.13 0.15 0.13 0.07 0.05 0.02 0.04 0.05
PDF 0.07 0.09 0.08 0.05 0.04 <0.01 <0.01 <0.01
Parton shower 0.65 0.83 0.67 0.38 0.23 0.18 0.10 0.49
QED radiation 0.38 0.50 0.42 0.24 0.14 0.11 0.13 0.45
Colour reconnection 0.03 0.10 0.06 0.04 0.13 <0.01 <0.01 <0.01
Underlying event 0.04 0.11 0.09 0.05 0.13 0.22 <0.01 <0.01
Ren./Fac. scale 0.05 0.08 0.07 0.05 <0.01 <0.01 <0.01 <0.01 Lepton modelling [%/GeV]
Trigger efficiency 0.12 0.17 0.15 0.09 0.05 0.05 0.03 0.09
Reconstruction efficiency 0.06 0.08 0.10 0.06 0.01 0.01 <0.01 <0.01
Identification efficiency 0.15 0.16 0.11 0.16 0.06 0.13 0.10 0.03
Energy scale 0.08 0.10 0.21 0.05 0.13 <0.01 <0.01 <0.01
Energy resolution 0.08 0.12 0.17 0.04 0.02 0.22 <0.01 <0.01
Jet modelling [%/GeV]
Reconstruction efficiency 0.13 0.10 0.23 0.16 0.05 0.12 0.10 <0.01
Energy Scale 0.17 0.09 0.16 0.19 0.07 0.14 0.14 0.51
Energy resolution 0.03 0.10 0.08 0.04 0.07 <0.01 0.10 0.34
Vertex fraction 0.14 0.19 0.17 0.10 0.06 0.06 0.08 0.26
ETmiss modelling [%/GeV]
Cell out and soft terms 0.08 0.16 0.15 0.19 0.05 0.12 0.10 <0.01
Pile-up 0.03 0.11 0.09 0.04 0.13 <0.01 <0.01 <0.01
Photon modelling [%/GeV]
Identification efficiency 0.41 0.53 0.44 0.25 0.15 0.12 0.14 0.45
Energy scale 0.12 0.14 0.24 0.20 0.04 0.10 0.14 0.12
Energy resolution 0.12 0.13 0.25 0.12 0.05 0.10 0.08 0.34
b-tagging [%/GeV]
b-tag. efficiency 0.48 0.61 0.52 0.30 0.17 0.14 0.14 0.47
Mistag rate 0.04 0.11 0.09 0.05 0.13 0.22 <0.01 <0.01
e/γ backgrounds [%/GeV]
Zγ+jets 0.13 0.14 0.12 0.11 0.06 <0.01 <0.01 <0.01
W γ+jets 0.04 0.10 0.07 0.07 0.05 0.10 <0.01 <0.01
Multijets+γ 0.20 0.11 0.06 0.09 0.17 0.13 0.10 0.44
Dibosons+γ 0.04 0.08 0.07 0.07 0.01 <0.01 <0.01 <0.01
Single top+γ 0.25 0.48 0.34 0.15 0.15 0.13 <0.01 0.51
e→γmissidentification 0.21 0.32 0.24 0.09 0.08 0.06 0.13 0.49
Templates modelling [%/GeV]
Prompt photons 0.60 0.61 0.55 0.32 0.12 0.12 0.12 0.48
Hadron-fakes <0.01 0.35 0.14 0.05 0.08 0.05 <0.01 <0.01
Table 8.6: Breakdown of systematic uncertainties on σttγ¯ as a function of the energy in the transverse plane of the photon.
The observed increase of the detector modelling systematics is associated with the increase of statistical component of each uncertainty. In fact, these uncertainties have been determined from simulations, for which the amount of simulatedt¯tγ events decreases with increasingET(γ).
) [GeV]
γ
T( E
50 100 150 200 250 300
[% / GeV] γttfidσ/ γttfidσδ
0 0.2 0.4 0.6 0.8 1
1.2 Uncertainties
Signal ,γ µ , e , j
miss
ET
-tagging b
backgrounds γ
e/
Templates
= 4.59 fb-1
∫
Ldt = 7 TeV sFigure 8.9: Relative strength to the cross section of each component of systematic uncertainty.
8.4.2 Comparison with the theoretical prediction
The results have been compared to that of the Next-to-Leading-Order (NLO) theoretical pre-diction. Three Leading-Order (LO) calculations, normalised to the same NLO/LO fraction are used in the comparison. The LO prediction are obtained with WHIZARD interfaced to HERWIG withMadGraph interfaced to two different PS programs, PYTHIA and HERWIG. The comparison is shown in Fig. 8.10. It can bee seen that, overall, the agreement is good and it increases with the photon-ET. For low-ET photons (ET(γ) < 30 GeV) the comparison shows consistent discrep-ancies with all predictions. However, the statistical fluctuations may contribute considerably to those discrepancies.
The (small) difference with respect to the theoretical prediction of the cross section seen in the inclusive measurement can be, thus, attributed to the low-ET region. In this region, the definition of the photon isolation may play a more important role. In fact, the NLO calculation uses a different definition of photons with respect to that used in the experimental measurement. The main difference arises in the treatment of collinear andinfra-red divergencies. The theory uses a clustering algorithm to define the photon which is considered to be infra-red safe. The photon definition used in this analysis uses a minimum-pTrequirement upon the tracks entering in thepisoT calculation. Therefore, it cannot be excluded these differences are due to this different definition of photons.