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The multijet background is mainly composed of events with jets misidentified astightleptons, jets with associated photon production and photons resulting from jet fragmentation. This background is estimated using a control sample in data. This control sample is characterised by relaxed identification and isolation criteria imposed on the lepton. This method is referred to as thematrix method[150]. A two step approach is used: firstly, the control sample with relaxed identification criteria on the leptons, is determined; secondly, the amount of prompt-photons within this sample is determined. The following sections explain in more details the two steps.

6.3.1 Definition of the control sample

For simplicity, isolated leptons are called real leptons, and jets misidentified as leptons, or non-isolated leptons that pass the identification and isolation criteria, are calledfake leptons. A control sample based on the t¯t selection requirements is defined on data. The difference with respect to the nominal selection is that the lepton identification criteria, defined in Sec. 3.5, are replaced with relaxed requirements. The rectangular cuts on the shower shapes defining the electron are widened, and the isolation requirement for both electron and muons is discarded. This event selection is

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Figure 6.12: The electron (muon) transverse energy (momentum) against the invariant mass of the reconstructed electron- (muon-) photon is shown for the electron (muon) channel on the left (right). The invariant mass cut around theZ-boson mass is not applied. The continuous vertical lines indicate the invariant mass window of±15GeV around theZ-peak, while the dotted vertical lines indicate the ±5 GeV window. For each plot, the horizontal continuous line indicates the minimum electron-ET cut (20 GeV) applied to the selection, while the horizontal dotted line indicates the minimum muon-pTrequirement (25 GeV).

calledloose selection and containsNloose events. The corresponding lepton’s definition is refereed to as a loose lepton. The nominal selection requirements defines a second sample as being tight and containingNtight events. The method makes the assumption that the total number of events in either samples is linear with respect to the number of real and fake leptons. The linearity for the loose sample can be expressed as:

Nloose=Nrealloose+Nfakeloose (6.9) withNrealloose and Nfakeloose being the number of events within the samples using the loose and tight lepton definitions respectively. Considering the probability for a real loose lepton to be identified as tight (freal) and the probability for a fake loose lepton to be identified as a tight fake lepton (fˆfake), the linearity in the tight sample can be expressed as:

Ntight =Nrealtight+Nfaketight =frealNrealloose+ ˆffakeNfakeloose (6.10) From Eq. 6.9 and Eq. 6.10 it follows that the number of fake leptons passing the tight selection (Nfaketight) is:

Nfaketight =

fake freal−fˆfake

Nloosefreal−Ntight

(6.11) TheNtight includes photons defined by thet¯tγ selection criteria.

6.3.2 Extraction of the multijet plus photon background

Kinematic-related and acceptance-based weights are applied to the Nfaketight sample, in order for the estimation to describe correctly the shape of reconstructed objects. However, the application

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Figure 6.13: The extraction of the Multijet+γ background, withET(γ)>20 GeV, for the electron (muon) channel is shown on the left (right). The data points correspond to the events passing the loose selection requirements before application of kinematic and acceptance weights. The last bin contains any overflow.

Loose sample hadron-fakes [events] Fraction [%]

Electron Channel 127.42±27.89 71.59±15.67 Muon Channel 246.88±40.77 94.23±15.56

Table 6.6: Estimates of hadron fakes within the loose sample selection. The fraction of hadron fakes for each channel is also shown. Uncertainties are statistical⊕systematic.

of event weights precludes the extraction of prompt-photons within the sample as it is based on the assumption that events in data are Poisson-distributed. Moreover, the validity of the asymptotic properties of the likelihood ratio method cannot be guaranteed for minimisations of binned distributions of small sizes.

The cut and count approach, described in App. D.5, is used instead. This approach determines the fraction of hadron-fakes from a given data binned distribution without constraining events within each bin to be Poisson-distributed. The cost of increased uncertainty, due to the chosen method, is overwhelmed by the statistical uncertainty, due to the small size of data candidates in this region.

At first, the fraction of hadron fakes within the control sample is estimated, see Tab. 6.6. The resultingpisoT distributions are shown in Fig. 6.13. Secondly, the estimated fractions are applied to the reweighed candidates of the Multijet+γ.

The total multijet plus photon background is estimated to be3.9±1.7 events in the electron channel and1.6±2.8 events in the muon channel.

Systematic Uncertainties

Systematic uncertainties for the Multijet+γ background comprise a 50% and 20% uncertainty in the electron and muon channels respectively, and are driven by the uncertainty of the matrix method [150]. The uncertainty on the extraction of prompt-photons is estimated to be 9.1% and

4.3% for the electron and muon channels respectively. It is determined from the fluctuations of the pisoT distribution for the hadron-fakes, details are given in App. D.5. Overall, the statistical uncertainty dominate across the entireET(γ) range.