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\section{Signal extraction} |
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%\label{sec:gen} |
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\subsection{Z+jets background fraction} |
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After applying "Official Tight" selection on electron decaying from W, there is still a significant fraction of Z+jets events passing selection, due to two orders of magnitude bigger cross section of the background processes. In this section we describe a method to estimate fake rate coming from Z+jets background, which has a significant contribution in channels where $W^{\pm}$ decays into $e^{pm}$ and neutrino. |
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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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The probability to misidentify a jet as a muon is very low while for |
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the case of the electron, $\pi^0$ in jets can be misidentified as |
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electrons. When considering the subtraction of the background in this |
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analysis, we will mainly concentrate on the final state where the $W$ |
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is decaying to an electron. For the muon case, the subtraction can be |
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done using Monte Carlo sample and assigning a large error on this |
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estimation. |
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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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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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\subsection{Z+jets background fraction} |
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The main background remaining even after having applied all our selection |
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in the case of the $W$ decaying to electron is the $Z+jets$ |
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production. As signal and background have a \Z boson in the final |
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state, we will concentrate on the third lepton which is an electron in |
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this study. |
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In order to select the \Z candidate in the events, we apply loose |
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criteria. The loose sample contain a given number of signal events |
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which contains a third isolated electron and a given number of |
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background events which do not contains a third isolated |
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electron. When we apply the tight criteria the fraction of signal and |
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background events is changing according to the efficiency of the |
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criteria. This can be expressed by this formula: |
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\begin{eqnarray} |
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N_{loose} & = & \hspace*{0.9cm} N_e + \hspace*{0.9cm} N_{j} \\ |
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N_{tight} & = & \epsilon_{tight} N_e + p_{fake} N_{j} |
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\end{eqnarray} |
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Where $N_{loose}$ and $N_{tight}$ are the numbers of events in |
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the loose and tight samples, respectively, $N_e$ is the number of events with a third |
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isolated electron, $N_j$ is the number of events without a third |
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isolated electron, $\epsilon_{tight}$ is the efficiency of the tight |
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criteria on electron, $p_{fake}$ is the probability for a jet identified |
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as a loose electron to be also identified as a tight electron. By |
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solving this set of equations we obtain: |
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$$ |
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N_e = \frac{N_{tight}-p_{fake} N_{loose}} { \epsilon_{tight} -p_{fake}} \ \ \ \mbox{and} \ \ \ |
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N_{j} = \frac{ \epsilon_{track} N_{loose} - N_e}{ \epsilon_{tight} -p_{fake}} |
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$$ |
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The estimation of $\epsilon_{tight}$ and $p_{fake}$ can be done using control |
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samples, containing electrons and jet respectively with high purity. The Tag and probe |
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method is used to determine signal efficiency $\epsilon_{tight}$. The rate |
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will be derived from $Z \to e^+e^-$ samples. In the following section we |
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describe the method used to determine $p_{fake}$. |
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\subsection{Determination of $p_{fake}$} |
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As the events will be most of the time triggered by the leptons coming |
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from \Z boson, we assume that the third lepton is unbiased toward |
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trigger requirement. Ideally we need a sample of pure multi-jet events |
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in order to compute the probability for a jet identified as a loose |
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electron to be also identified as a tight electron. In selecting such |
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a sample in data, one has to avoid any bias from the trigger |
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requirements on the loose electron candidate. |
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%Such sample will not |
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%exist in data as they will be bias by the trigger requirement. |
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From a sample of multi-jet events triggered by an ``OR'' of multi-jet |
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triggers, we will select loose electron candidates that are not |
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matched to any of the triggering object |
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%we will reject the object matched with the triggering |
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%objects. This will allow us to have a unbiased sample of multi-jet |
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%events. For the purpose of the study, we have used CSA07 Gumbo |
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%samples, with Pythia ID filtering in order to keep only events from |
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%photon+jets, QCD and minimum bias events. |
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The removal of the object matched with the triggering object is done |
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using a matching cone of $\Delta R =0.2$. "Simple Loose" selection is |
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applied to each reconstructed electron from this sample of jets from |
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QCD and photon+jet. Then the tight criteria is applied on such loose |
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electrons and the $p_{fake}$ is simply the ratio of this two |
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population. This ratio, given as a function of $Pt$ and $\eta$, is |
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showed in plots \ref{fig:qcd_zjet_est}. |
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\subsection{Determination of $\epsilon_{tight}$} |
