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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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\label{sec:SignalExt} |
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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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After applying "Official Tight" selection on electron decaying from W, there |
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is still a significant fraction of Z+jets events passing selection, due to |
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two orders of magnitude bigger cross section of the background processes. |
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In this section we describe a method to estimate fake rate coming from Z+jets |
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background, which has a significant contribution in channels where $W^{\pm}$ |
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decays into $e^{pm}$ and neutrino. |
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|
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Z bosons from Z+jet events will be with the same efficiency reconstructed with |
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a Z mass between a $\pm 20$ window. Background rate is already reduced after applying |
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"Simple Tight" selection to the W electron. We first apply "Tight Loose" selection for |
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$W\pm$ electron, while later we apply "Simple Tight" selection to count number of events |
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passing selection in both cases. Number of events are named respectively, $N_l$ and $N_t$. |
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|
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$Nl$ contains an unknown numbers of signal and background events, $N_s$ and $N_b$, so a |
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number of "Simple Loose" events is $Nl=Ns+Nb$ Number of events passing "Simple Tight is |
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$N_t=\epsilon_s * N_s + \epsilon_b * N_b$. It is possible to calculate background fraction |
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$N_b/(N_s+N_b)$ if we are able to estimate $\epsilon_s$ and $\epsilon_b$, signal and background |
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efficiency. Their estimation is done using control data samples, which contain either electrons |
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or jets with high purity. Tag and probe method is used to determine signal efficiency $\epsilon_b$. |
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The rate will be derived from $Z \to e^+e^-$ samples. In the following text we describe method |
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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 |
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estimation of Z+jets jet selected as $W\pm$ electron. The samples used in analysis are CSA07 |
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Gumbo samples, with Pythia ID filtering so that only events from photon+jets, QCD and minimum |
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bias event are used. As the sample contains event classes with different event weight, separated |
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by $\hat{P_t}$ value and Pythia ID, we calculate weight as $w_i=\frac{\sigma_i}{N_i}$ where |
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$\sigma_i$ and $N_i$ are respective cross section and event number for event class with the |
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same event weight. "Simple Loose" selection is applied to each reconstructed pixel-matched GSF electron found in event. |
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In case of having more than one reconstructed electron objects per event passing selection, |
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we appy the same weight to each. Efficiency, defined as a ratio of number of objects passing "Simple Tight" |
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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 |
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control sample. After requiring all events to pass a HLT1jet trigger path, which cuts on a 200 GeV Pt treshold |
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of the single jet, there is significant drop of the efficiency in the area of interest, 20-100 GeV, as shown |
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in the plot \ref{fig:qcd_zjet_est-missing}. First assumption, that removing objects within a $0.1 \Delta R$ cone to |
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a HLT Jet object which triggered the HLT1jet path would restore efficiency as seen without trigger requirement, |
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prooved insufficient, with efficiency still being significantly biased in the 20-100 GeV range. We assume that |
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this is due to other jets in the event having similar energy to the triggering jet, so with the leading jet of |
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200 GeV Pt or higher this effectively removes events with jets from the lower Pt range. New attempt was made to |
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remove all reconstructed electrons from the selection within the $\Delta R$ cone with any of the jets triggering |
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HLT1jet, HLT2jet, HLT3jet and HLT4jet trigger paths, with respective jet tresholds 200, 150, 85 and 60 GeV. |
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Since the tresholds are lower, we assume to have more events with real jets in low Pt range (50-100 GeV). |
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Resulting efficiency is shown in the plot \ref{fig:tight_eff_gumbo-missing2}. |
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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, assuming we have found a \Z boson that has fullfilled all |
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our requirements. |
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In order to select the \W 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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|
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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 jets respectively with high purity. The Tag and Probe |
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method is used to determine the 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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\begin{figure}[bt] |
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\begin{center} |
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\scalebox{0.8}{\includegraphics{figs/tight_eff_gumbo.eps}} |
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\caption{Efficiency of "Simple Tight" over "Simple Loose" reconstructed fake electrons on Gumbo sample |
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(QCD, photon+jets and minimum-bias events). Distributions are shown in $P_t$ and $\eta$.} |
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\label{fig:tight_eff_gumbo} |
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\scalebox{0.6}{\includegraphics{figs/tight_eff_gumbo.eps}} |
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\caption{Fraction of electron candidates passing the tight criteria |
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in QCD event. No trigger requirement has been applied.} |
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\label{fig:qcd_efftight_noHLT} |
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\end{center} |
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\end{figure} |
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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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|
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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 is showed as a function of \pt and $\eta$ |
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for all loose electrons in QCD events in Figure~\ref{fig:qcd_efftight_noHLT}. |
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%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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|
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%for the last part, it is still to be seen if the method works, though. |
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\subsection{Determination of $\epsilon_{tight}$} |
