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\section{Signal extraction} |
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%\label{sec:gen} |
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\label{sec:SignalExt} |
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Two kind of background are affected this analysis: background having |
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already a $Z$ boson in the final state such as $Z+jets$ and |
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$Z+b\bar{b}$, background without a $Z$ boson such as $W+jets$ and |
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$t\bar{t}$. The first one will be peaking as the signal in the $Z$ |
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mass distribution while the second should be flat.As a starting point, |
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we will use this properties to separate the two background. |
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|
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\subsection{Study of non peaking background} |
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In order to measure this background, a fit of the signal and |
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background is done. In order to fit the signal peak we use a Gaussian |
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convulated with a Breit-Wigner. The background is fitted by a line. |
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An example of the fit of the distribution composed by the sum of |
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signal and background for the 3 electrons final state is shown on |
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figure~\ref{fig:ZFit}. |
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\begin{figure}[!bp] |
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\begin{center} |
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\scalebox{0.4}{\includegraphics{figs/FitBkg3eTight.eps}} |
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\caption{$Z$ mass distribution which contains the sum of signal and background on which a fit is performed to extract the number of non peaking background events within the 81 GeV and 101GeV.} |
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\label{fig:ZFit} |
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\end{center} |
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\end{figure} |
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|
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The comparison between the Monte Carlo information and the value |
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obtain by the fit for a $Z$ mass range [81,101] GeV is given in |
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table~\ref{tab:FitVsMC}. |
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|
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\begin{table}[!tb] |
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\begin{center} |
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|
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\begin{tabular}{|l|c|c|c|c|c|c|c|} \hline |
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Channel & $Z+jets$ & $Zb\bar{b}$ & $t\bar{t}$ & $W+jets$ & $t\bar{t}$ + $W+jets$ & Fit result \\ \hline |
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$3e$ Loose & 196.5 & 67.4 & 35.7 & 0 & 35.7& 37.8 \\ \hline |
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$3e$ Tight & 78.9 & 38.5 & 28.1 & 0 & 28.1 & 32.9 \\ \hline |
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$2\mu 1e$ Loose & 189.6 & 52.6 & 4.7 & 0 & 4.7 & 5.7 \\ \hline |
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$2\mu 1e$ Tight & 63.1 & 18.2 & 1.3 & 0 & 1.3 & 1.5 \\ \hline |
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$2e1\mu$ & 10.4 & 9.1 & 30.7 & 2.9 & 33.6 & 29.2 \\ \hline |
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$3\mu$ & 1.9 & 7.7 & 0.7 & 0 & 0.7 & 0\\ \hline |
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\end{tabular} |
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|
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\end{center} |
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\caption{Comparison between monte carlo expectation for the analysis and the results of the fit for the non peaking background. Number of event are integrated between [81,101] GeV. The Loose and Tight criteria apply so far, for final state where $W\rightarrow e\nu$. One has to consider that this study as been perform on a smaller sample than the other part of the analysis a 10\% statistics error as to be counted until the study is performed on the whole samples. |
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} |
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\label{tab:FitVsMC} |
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\end{table} |
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|
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|
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\subsection{Study of peaking background} |
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\label{sec:D0Matrix} |
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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 misidentify as |
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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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is decaying to an electron. The same studies is still on going for the |
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muon case. |
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|
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\subsection{Z+jets background fraction} |
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The main background remaining even after have apply all our selection |
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\subsubsection{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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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 $N_{loose}$/$N_{tight}$ is respectively the number of events in |
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the loose/tight sample, $N_e$ is the number of events with a third |
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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 identify |
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as a loose electron to be also identify as a tight electron. By |
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solving this equations we obtain: |
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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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$$ |
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N_e = \frac{N_{tight}-p_{fake} N_{loose}} { \epsilon_{tight} -p_{fake}} \ \ \ \mbox{and} \ \ \ |
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N_{j} = \frac{ \epsilon_{track} N_{loose} - N_e}{ \epsilon_{tight} -p_{fake}} |
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N_{j} = \frac{ \epsilon_{tight} N_{loose} - N_e}{ \epsilon_{tight} -p_{fake}} |
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$$ |
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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 jet respectively with high purity. Tag and probe |
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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 text we |
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describe method used to determine $p_{fake}$. |
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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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\subsubsection{Determination of $p_{fake}$} |
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|
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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 identify as a loose |
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electron to be also identify as a tight electron. Such sample will not |
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exist in data as they will be bias by the trigger requirement. |
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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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\begin{figure}[bt] |
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\begin{center} |
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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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|
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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 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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|
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The removal on the object matched with the triggering object is done |
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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 electrons from this sample of jets from |
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QCD and photon+jet. Than the tight criteria is applied on such loose |
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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 given as a function of $Pt$ and $\eta$, is |
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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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|
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\subsection{Determination of $\epsilon_{tight}$} |
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\subsubsection{Determination of $\epsilon_{tight}$} |
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TO BE WRITTEN... SRECKO??? |
