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- Systematics on selection\\ |
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- On Cross Section for MC\\ |
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- On D0Matrix method\\ |
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In this section, we will assign systematics errors to this |
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analysis. The assignement of systematics is expected to be |
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conservative. |
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|
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\subsection{Experimental Systematics} |
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|
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The experimental systematics errors expected that will affect the |
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signal and standard model background are: |
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\begin{itemize} |
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\item For trigger selection, a systematics of 1\% is assigned. Even |
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though the efficiency of the signal is greater than 99\%, the trigger |
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path used for both muons and electron expect the leptons to be |
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isolated. As the isolation depends on the occupancy of the events, |
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the alignment of the tracker (when considering tracker isolation |
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variables) and noise in the calorimeters (when considering a |
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calorimetric isolation), this value is expected to be conservative. |
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|
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\item 2\% error is assigned on electron/muons reconstruction. Both of |
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them are link to alignment of the track in order to reconstruct the |
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leptons. A systematics of 2\% is assigned for the determination of |
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the charge of the electron candidate while 1\% for the muon as the |
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electron problem is coming from the high probability of emission of |
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photons. |
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|
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\item A systematics of 1\% will be assigned for the measurement of |
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the lepton energy. |
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|
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\item 4\% of systematics are considered for the electron |
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identification, 2\% for the muon case. |
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\end{itemize} |
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|
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The PDF uncertainties on the signal has been determined in~\cite{OldNote}. |
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The uncertainty was found to be: |
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\begin{equation} |
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\Delta \sigma_+ ^{tot} = 3.9\% \hspace{0.9cm} \Delta \sigma_- ^{tot} = 3.5\% |
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\end{equation} |
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|
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The luminosity error is expected to be 10\%. |
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|
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The table~\ref{tab:sys} resume all systematics considered. |
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|
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\begin{table}[!tb] |
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\begin{center} |
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\begin{tabular}{|l|c|c|} \hline |
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Systematics Source (in \%) & Cross Section & Signficance \\ \hline |
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Luminosity & 10.0 & - \\ |
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Trigger & 1.0 & 1.0\\ |
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Lepton Reconstruction & 2.0 & 2.0\\ |
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Electron Charge Determination &2.0& 2.0\\ |
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Muon Charge Determination &1.0& 1.0\\ |
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Lepton Energy Scale& 1.0& 1.0\\ |
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Electron Identification& 4.0 &4.0\\ |
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Muon Identification& 2.0 &2.0\\ |
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PDF Uncertainties& - & + 3.9\\ |
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& & - 3.5 \\ \hline |
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\end{tabular} |
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|
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\end{center} |
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\caption{Systematics in percent for $pp\rightarrow WZ$ cross section measurement and significance estimation for 1 fb$^-1$ of integrated luminosity.} |
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\label{tab:sys} |
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\end{table} |
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|
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|
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\subsection{Background Substraction Systematics} |
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|
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We present here, the result for the case where the $W$ is decaying via |
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an electron. |
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|
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Two steps will be used to substract the different background: first, |
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the non peaking background should be substracted, then the background |
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$Z+jets$ will be determine using the method described |
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in~\ref{sec:D0Matrix}. |
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|
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From the fit, we will consider a systematics error of 10\%. |
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|
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If we consider an error of 5\% on the fake rate and an error of 2\% |
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on the efficiency on signal to go from loose to tight criteria, we can |
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calculate the error on the estimated background as follow: |
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\begin{equation} |
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\Delta N_j ^{t} = \sqrt{(\frac{(p[N_{t} - p(N_{l}+N_{t})])}{(\epsilon -p)^2})^2 \times \Delta \epsilon^2 |
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+(\frac{(\epsilon[\epsilon(N_{l}+N_{t})-N_{t}]}{(\epsilon -p)^2})^2 \times \Delta p^2 |
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+ (\frac{(p\epsilon)}{(\epsilon -p)})^2 \times \Delta N_{l}^2 + (\frac{[p(\epsilon -1 )]}{(\epsilon -p)})^2 \times \Delta N_{t}^2} |
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%\Delta N_j ^{tight} = \frac{\sqrt{(p_{fake}[N_{tight} - p_{fake}(N_{loose}+N_{tight})])^2 \dot \Delta \epsilon^2 |
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%+(\epsilon[\epsilon(N_{loose}+N_{tight})-N_{tight}]^2 \dot \Delta p_{fake}^2 |
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%+ (p_{fake}\epsilon)^2 \dot N_{loose} + [p_{fake}(\epsilon -1 )]^2 \dot N_{tight}}}{\epsilon_{tight} - p_{fake}} |
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\end{equation} |
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where $N_{t}$,$\Delta N_{t}$ and $N_{l}$,$\Delta N_{l}$ represents |
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respectivement the number of events in the tight sample and in the |
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loose sample and their errors.$\epsilon$ represent efficiency for a |
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loose electron to pass the tight criteria, $\Delta \epsilon$ the error |
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on this value.$p$ gives the probability for a fake loose electron to |
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pass also the tight criteria and $\Delta p$ its error. |
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|
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The overall error from the background substraction is 18\%. |
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|
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\subsection{Summary of Systematics} |
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|
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In table~\ref{tab:FullSys}, the systematics errors are expressed for |
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each channels. |
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|
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\begin{table}[!tb] |
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\begin{center} |
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\begin{tabular}{|l|c|c|} \hline |
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Channels & Cross Section & Signficance \\ \hline |
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3e & 8.4\% +10\% = 13.1\% & +9.3\% / - 9.2\% \\ |
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2e1$\mu$ & 7.7\% +10\% = 12.6\% & +8.7\% / - 8.5\% \\ |
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1e2$\mu$ & 6.5\% +10\% = 11.9\% & +7.6\% / - 7.4\% \\ |
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3$\mu$ & 5.5\% +10\% = 11.4\% & +6.7\% / - 6.5\% \\\hline |
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\end{tabular} |
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|
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\end{center} |
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\caption{Systematics per channels in percent for $pp\rightarrow WZ$ cross section measurement and significance estimation for 1 fb$^-1$ of integrated luminosity. These systematics do not include the background substraction.} |
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\label{tab:FullSys} |
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\end{table} |
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|
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\subsection{Background Substraction} |
