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Z bosons from Z+jet events will be with the same efficiency reconstructed with a Z mass between a $\pm 20$ window. Background rate is already reduced after applying "Simple Tight" criteria to the W electron. We first apply selection for W electron to "Tight Loose", while later we apply "Simple Tight" selection to count number of events passing selection in both cases. Number of events are named respectively, $N_l$ and $N_t$. |
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$Nl$ contains an unknown numbers of signal and background events, $N_s$ and $N_b$, so number of "Simple Loose" events is $Nl=Ns+Nb$. Applying the "Simple TIght" selection. Number of events passing "Simple Tight: is $N_t=\epsilon_s * N_s + \epsilon_b * N_b$. It is possible to calculate background fraction $N_b/(N_s+N_b)$ if we are able to estimate \epsilon_s and \epsilon_b, signal and background efficiency. Their estimation ca be done using control data samples, containing electrons and jet with high purity. Tag and probe method is used to determine signal efficiency $\epsilon_b$. The rate will be derived from Z->e^+e^- samples. In the following text we describe method used to determine \epsilon_{B}. |
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$Nl$ contains an unknown numbers of signal and background events, $N_s$ and $N_b$, so number of "Simple Loose" events is $Nl=Ns+Nb$. Applying the "Simple TIght" selection. Number of events passing "Simple Tight: is $N_t=\epsilon_s * N_s + \epsilon_b * N_b$. It is possible to calculate background fraction $N_b/(N_s+N_b)$ if we are able to estimate $\epsilon_s$ and $\epsilon_b$, signal and background efficiency. Their estimation ca be done using control data samples, containing electrons and jet with high purity. Tag and probe method is used to determine signal efficiency $\epsilon_b$. The rate will be derived from $Z \to e^+e^-$ samples. In the following text we describe method used to determine $\epsilon_{B}$. |
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\subsection{Method description} |
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We apply "Simple Loose" selection on jets from QCD and photon+jet control samples for fake rate estimation of Z+jets jet selected as $W\pm$ electron. The samples used in analysis are CSA07 Gumbo samples, with Pythia ID filtering so that only events from photon+jets, QCD and minimum bias event are used. As the sample contains event classes with different event weight, separated bt \hat{Pt} value and Pythia ID, we calculate weight as $w_i=\frac{\sigma_i}{N_i}$ where $\sigma_i$ and $N_i$ are respective cross section and event number for event class with the same event weight. "Simple Loose" selection is applied to each reconstructed object reco::pixelMatchGsfElectrons. In case of having more than one reconstructed electron objects per event passing selection, we appy the same weight to each. Efficiency, defined as a ratio of number of objects passing "Simple Tight" and "Simple Loose" selection, given as a function of $Pt$ and $\eta$, is showed in plots \ref{fig:qcd_zjet_est}. |
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We apply "Simple Loose" selection on jets from QCD and photon+jet control samples for fake rate estimation of Z+jets jet selected as $W\pm$ electron. The samples used in analysis are CSA07 Gumbo samples, with Pythia ID filtering so that only events from photon+jets, QCD and minimum bias event are used. As the sample contains event classes with different event weight, separated bt $\hat{P_t}$ value and Pythia ID, we calculate weight as $w_i=\frac{\sigma_i}{N_i}$ where $\sigma_i$ and $N_i$ are respective cross section and event number for event class with the same event weight. "Simple Loose" selection is applied to each reconstructed object reco::pixelMatchGsfElectrons. In case of having more than one reconstructed electron objects per event passing selection, we appy the same weight to each. Efficiency, defined as a ratio of number of objects passing "Simple Tight" and "Simple Loose" selection, given as a function of $Pt$ and $\eta$, is showed in plots \ref{fig:qcd_zjet_est}. |
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Since the data collected by the CMS is filtered by the trigger, the trigger bias study was done one the Gumbo control sample. After requiring all events to pass a HLT1jet trigger path, which cuts on a 200 GeV Pt treshold of the single jet, there is significant drop of the efficiency in the area of interest, 20-100 GeV, as shown in the plot \ref{fig:qcd_zjet_est}. First assumption, that removing objects within a $0.1 \Delta R$ cone to a HLT Jet object which triggered the HLT1jet path would restore efficiency as seen without trigger requirement, prooved insufficient, with efficiency still being biased in the 20-100 GeV range. We assume that this is due to other jets in the event having similar energy to the triggering jet, so with the leading jet of 200 GeV Pt or higher this effectively removes events with jets from the lower Pt range. New attempt was made to remove all reconstructed electrons from the selection within the $\Delta R$ cone with any of the jets triggering HLT1jet, HLT2jet, HLT3jet and HLT4jet trigger paths, with respective jet tresholds 200, 150, 85 and 60 GeV. Since the tresholds are lower, we assume to have more events with real jets in low Pt range (50-100 GeV). Resulting efficiency is shown in the plot \ref{fig:qcd_zjet_est}. |
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