Data Driven Methods

In addition to the background MC, two background processes are modeled from aux-iliary measurements. One is the measurement of QCD multijets in data. Since multi-jet production is very difficult to model with MC, the measurement needed is made on data. To estimate the QCD multijet background, two separate methods are used: matrix method [139] and so-called anti-electron model. The matrix method is used in both the e + jets and µ + jets channel as the default estimation. The anti-electron method is

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used as a cross-check QCD estimation in the e+ jets channel and used to estimate the systematic uncertainty based on QCD modelling. The second data driven estimation is of the normalization level of the W + jets background, the most significant background in the l+ jets channel.

5.4.1. QCD Multijets Estimation from the Matrix Method

The first method used to measure the QCD multijet production is known as the Matrix Method. The procedure uses the efficiency of tight and loose leptons in order to estimate weights for each lepton in data. This is the default method used to estimate the QCD multijets for this analysis. Events from QCD multijets are events which are assumed to contain fake leptons either from improperly isolated leptons from semi-leptonic b decays, mis-reconstructed jets or in the electron case, photon conversions.

For each of the two channels, a separate event selection is made. In the first case, the original event selection is performed. The first case uses thetight definition of the lepton.

The second event selection uses a loose definition of the lepton. In both cases an event weight is given to the data. The weight corresponds to whether the event contains a loose or tight definition of the lepton. When adding all of the weights for a given sample, the total yield and corresponding shape can be obtained for QCD multijets background.

The definitions for tight leptons are given by the nominal event and object selections found in Section 4.2. The loose definitions are the same as the tight definitions except for the following modifications:

• muon: no isolation requirement (both p^cone_T and E^cone_T are not used),

• electron: a looser isolation requirement from the p_T corrected E^cone_T < 6 GeV (in-stead of 3.5 GeV), a type medium electron with an additional requirement of a reconstructed track with a b-layer hit in the inner detector, and the use of medium missing transverse energy requirement at the event level (instead of tight 6E_T).

The number of events in the two separate samples are given by:

N^loose = N_real^loose+N_{f ake}^loose, (5.1) N^tight = _realN_real^loose+_{f ake}N_{f ake}^loose, (5.2) where the f ake and real are the two efficiencies for fake and real QCD events. They are defined by:

_{f ake/real} = N_{f ake/real}^tight

N_{f ake/real}^loose . (5.3)

The fake efficiency is calculated from an enriched QCD sample obtained when using a low transverse mass m^T_W region in the µ + jets channel, which contains a significant amount of QCD events. m^T_W is defined in Equation 4.8.

5. Modelling of Signal and Background Processes

The resulting distribution for inclusive 1 jet events can be seen in Figure 5.1, where an abundance of QCD events is visible in the low transverseW mass (m^T_W) region.

Figure 5.1.: Control regions of the low m^T_W region in both (left): µ + jets and (right):

e + jets for the matrix method background estimation for QCD multijets production. The abundance of QCD events can be seen in this region.

Figures taken from [140].

In thee + jets channel, the fake efficiencies were determined from the low 6E_T control region (5 < 6E_T <20 GeV).

The real efficiency is calculated with the tag and probe method in a sample ofZ →µ⁺µ⁻ or Z → e⁺e⁻ events, similarly to the trigger and identification efficiencies for lepton objects. The tag and probe method uses an identified lepton (“tag”) and searches for the second lepton from the Z decay (“probe”).

The resulting weights applied to the data are given to events where the loose lepton also fulfills the tight requirements:

w^tight_{M M} = εreal·εf ake

ε_real−ε_{f ake} (5.4)

and when the loose electron fails the tight requirements:

w_{M M}^loose= (εreal−1)·εf ake

ε_real−ε_{f ake} (5.5)

The total number of events which contain at least a loose lepton receive a weight. The loose leptons obtain a small negative weight, whereas events which contain a lepton which satisfies both tight and loose definitions, obtain a positive weight. By adding all of these events, the total shape and normalization of the QCD multijets background is estimated.

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5.4. Data Driven Methods

5.4.2. QCD Multijets Estimation from the Anti-Electron Model

In the electron channel, the so-called “anti-electron model”¹is employed to estimate the QCD multijets shape uncertainty which is accounted for in the total systematics uncer-tainty of this method. The model uses the same selection as the electron, except inverts the tight isolation, resulting in an “anti-electron”. As a result, the sample is completely orthogonal to the dataset used for the analysis. The resulting fit to data, along with the other MC processes determines the overall normalization of the sample. From this fit, an extrapolation of the shape is made into the signal region, giving the shape and normalization for QCD multijets in data.

5.4.3. W + Jets Normalization

The second data driven estimate made for the modelling of background processes is the estimation of the normalization of W + jets. The MC is used to model the shape and the data is used to normalize the overall contribution of W + jets in background. The normalization estimation is performed using theW charge asymmetry measurement [141].

The asymmetry arises from W bosons which are created charge asymmetrically (more W⁺ than W⁻) at the LHC since they are produced by qq¯annihilation. The W boson then decays leptonically leaving a charged lepton which can be identified. As a result, the charge imbalance is measured giving the overall normalization of the W + jets events.

Using the assumption that all other physics processes produce symmetrically charged leptons, the number of W⁺ andW⁻ can be determined using the formula:

NW++NW−=

rM C+ 1 r_{M C}−1

(D⁺−D⁻), (5.6)

where D⁺ and D⁻ are the number of events in data which pass the full event selection before b-tagging with a positively charged or negatively charged lepton respectively. The variable rM C is the cross section ratio of W⁺ production divided by W⁻ production determined in MC. The results of this measurement are applied to the overall normalization of W + jets background in the 4 inclusive jet channel. The resulting SF determined in the 4 jet inclusive jet bin is found in Table 5.1. The largest uncertainties of the method arise from uncertainties in the parton density functions, jet energy scale, and heavy flavour fraction in W + jets events.

N_jets µ+ jets pretag µ+ jets tagged e+ jets pretag e+ jets tagged

≥ 4 0.80±0.11 0.79±0.18 0.96±0.14 0.89±0.20

Table 5.1.: Normalization factor applied to W + jets events in MC. The numbers are obtained from theW charge asymmetry measurement made at ATLAS.

1explained in further detail in Ref. [44]

5. Modelling of Signal and Background Processes

5.4.4. W + Jets Heavy-to-light Normalization

To account for the proper heavy-to-light ratio inW + jets events, studies were performed on data to check the proper fraction ofb,cand light events. The study is performed using the W + 1 and W + 2 jet bins. Using three numbers: the number of tagged events in W+ 1 andW+ 2 jet bins and the number ofW+ 2 events before b-tagging, a relationship between tagged and un-tagged events for b¯b, c¯c and W c scenarios can be established in data. The resulting scale factors are found to be:

SF_{W b}¯b/W c¯c= 1.63±0.76 (5.7)

and for the fraction of W cevents:

SF_{W c} = 1.11±0.35 (5.8)

compared to the original alpgen MC. To keep the overall normalization, W + light jet samples are rescaled down to keep the total number of events the same.

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