7.5 Correlations and likelihood modelling
8.1.1 Systematic uncertainties
Figure 8.2: Negative logarithm of the profile likelihood as a function of the ttγ¯ fiducial cross section σt¯tγ ×BR with (solid line) and without (dashed line) free nuisance parameters associ-ated with the systematic uncertainties. The horizontal dotted line corresponds to a value of
= 0.5. Intersections of this line with the solid (dashed) curve give the ±1σ total (statistical only) uncertainty interval to the measured fiducialttγ¯ cross section.
see Fig. 8.3, is in excellent agreement with that obtained from the fit on data.
Thet¯tγ cross section times the Branching Ratio (BR) per lepton flavour, as defined in Chap. 4, is determined to be
σt¯tγ×BR = 63 ±8(stat.)+17−13(syst.)±1 (lumi.) fb (8.2) where BR is the ttγ¯ branching ratio in the single-electron or single-muon final state. A good agreement is found with the predicted cross sections [54, 56] of48±10 fband47±10 fbobtained from theWHIZARD and MadGraphMonte Carlo generators respectively after normalisation by the corresponding NLO/LOk-factors.
8.1.1 Systematic uncertainties
The total effect of each systematic uncertainty on the cross section is evaluated using ensemble tests with the method described in App. D.1.3. For each systematic uncertaintyi, pseudo-data are generated from the full likelihood while keeping all parameters fixed to their maximum likelihood estimates values except for the nuisance parameter associated to the systematic uncertainty source of interest. For each ensemble, a template fit is performed allowing all parameters of the likelihood (nuisance parameters, signal cross section) to vary. The variance of the obtained distribution of cross sections gives the uncertainty due to thei-th systematic uncertainty. This method has been validated against several others, which are thoroughly described in App. D.1. In the following, the effect on the cross section of each systematic component is reviewed in more details, while a summary of the breakdown is shown in Tab. 8.2.
20 40 60 80 100 120 140
Pseudo-experiments / pb
0 100 200 300 400 500 600 700 800
Pseudo-experiments Gaussian fit
L dt = 4.59 fb-1
=7 TeV, s
± mean = 61.98
± width = 8.20
Figure 8.3: Verification of the estimation of the statistical uncertainty on the cross-section mea-surement. Cross-section estimates are obtained from a set of 104 pseudo-experiments performed without the inclusion of systematic sources. Each pseudo-experiment is generated with the same amount of data as the dataset analyzed. The statistical uncertainty on the cross-section measure-ment is extracted from the width of a Gaussian fit (solid line).
The contribution to the systematic uncertainty on σttγ¯ due to the template shape modelling amounts to 7.6% in total. Of this, the background template shape modelling uncertainty amounts to 3.7% of the cross section, and the prompt-photon template uncertainty amounts to 6.6%.
The uncertainty on the t¯tγ cross section due to the modelling of the signal is estimated to be 8.4%. It is seen that the differences between MadGraphand WHIZARDamount to 1.7% of the total uncertainty, while the component of uncertainty due to the QED radiation modelling amounts to 1.7%. The effect of varied renormalisation and factorisation scales leads to an uncertainty of 1.1%
on the cross section. The effect on the choice of the Parton Shower (PS) model impacts the cross section with a 7.3% uncertainty. Smaller contributions due to the choice of colour reconnection model (0.2%) and underlying event (0.9%) settings are also included into the total uncertainty.
Systematic source Uncertainty, % Template modelling
Bck. template modelling: γ leakage 3.7
Signal template modelling 6.6
MC generator 1.7
Parton shower 7.3
QED FSR 3.4
Colour reconnection 0.2
Underlying event 0.9
Ren/Fac. scale 1.1
Photon identification efficiency 7.3
Photon scale 2.7
Photon resolution 4.0
Trigger efficiency 0.3
Reconstruction efficiency 0.5
Identification efficiency 1.2
Energy scale 0.3
Energy resolution 0.1
Trigger efficiency 1.7
Reconstruction efficiency 0.4
Identification efficiency 1.0
Momentum scale 0.3
Momentum resolution 0.7
Jet reconstruction efficiency 0.1
Jet energy scale 15.0
Jet energy resolution 6.5
Jet vertex fraction 2.6
b-tag efficiency 8.1
Mistag rate 1.1
Soft-jets and Cell-Out terms 0.3
QCD multijets+γ 1.5
Single top+γ 0.4
Table 8.2: Summary of the different systematic uncertainty contributions to theσt¯tγ cross section as obtained from ensemble tests.
The systematic uncertainty on the cross section due to photon modelling is 8.8%. It is estimated from the photon identification (7.3%) , the electromagnetic energy scale (2.7%) and the res-olution (4.0%) systematic uncertainties .
The systematic uncertainty on the cross section due to lepton modelling is 2.5%. It is esti-mated separately for the electron and muon channels from the lepton trigger (0.3% and 1.7%), reconstruction (0.5% and 0.4%) and identification (1.2% and 1.0%) efficiency uncertainties, as well as from those on the energy scale (0.3% and 0.3%) and resolution (0.1% and 0.7%).
The systematic uncertainty on the cross section due to jet modelling is 16.6%. It is estimated taking into account the following contributions. The largest effect comes from the energy scale (15.0%) uncertainty. The jet energy resolution uncertainty is estimated to 6.5% of the cross section.
The uncertainty on jet reconstruction efficiency (1.0%) and the jet vertex fraction uncertainty (2.6%) are also included.
The systematic uncertainty on the cross section due to b-tagging modelling is 8.2%. It is dominated by the contribution due to the efficiency (8.1%) with a small contribution due to the mistag probability (1.1%).
Systematic uncertainties on the energy scale and resolution of leptons, jets and photons are propagated to ETmiss. Additional contributions from low-pT jets (Soft terms) and from energy in calorimeter cells that are not included (Cell out) in the reconstructed objects (0.3%), as well as any dependence on pile-up (0.9%) are estimated to impact the cross section to 0.9% in total.
The effect of the luminosity uncertainty on the cross section amounts to 1.8%.
The total systematic uncertainty originating from processes that constitute a background to t¯t production with an additional final state photon as well as electrons misidentified as photons is estimated to be 7.7%. This uncertainty includes the following: electrons misidentified as photons (5.0%), W γ +jets (5.4%), as well as multijet+γ (1.5%), Zγ+jets (1.3%), diboson (0.4%) and single top+γ (0.4%) processes.
For backgroundestimatesobtained using simulation, uncertainties on the cross section predic-tions are taken into account. ForZγ+jets, single-top and diboson contributions the cross section systematic uncertainty is negligible with respect to the statistical uncertainty.