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\section{Systematic uncertainties} |
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\label{sec:systematic} |
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In this section, we estimate systematics uncertainties of the methods |
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used in this analysis. We follow the rule of making conservative estimates |
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throughout this section. |
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reconstruction, PDF, and luminosity are described below |
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|
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\begin{itemize} |
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\item {\it Trigger}: the trigger path used to select four categories require |
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leptons to be isolated. Though, the isolation criteria depends on the |
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occupancy of the sub-detectors, the alignment of the tracker (when |
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considering tracker isolation variables), and noise in the calorimeters (when |
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considering a calorimetric isolation), the trigger efficiency is |
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expected to be around 99\%, and therefore, a systematic uncertainty |
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is conservatively estimated as 1\%. |
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|
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\item {\it Reconstruction}: we assign 2\% systematic uncertainty per lepton |
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due to initial tracker alignment which is of paramount importance to |
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reconstruct leptons, 2\% and 1\% is assigned for the determination |
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of the charge of the electron and muon candidates, respectively. We assigned |
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a larger electron charge identification uncertainty due to much stronger |
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Bremsstrahlung energy loss which makes the charge identification more |
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difficult. |
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\item {\it Trigger}: the trigger path used to select four categories |
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require leptons to be isolated. Though, the isolation criteria |
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depends on the occupancy of the sub-detectors, the alignment of the |
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tracker (when considering tracker isolation variables), and noise in |
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the calorimeters (when considering a calorimetric isolation), the |
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trigger efficiency is expected to be around 99\%, and therefore, a |
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systematic uncertainty is conservatively estimated as 1\%. From the |
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current analysis of $Z\rightarrow l^+l^-$ in |
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CMS~\ref{Zmumu}~\ref{Zee}, the number of \Z events is estimated of the |
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order of 50k per 100 pb$^{-1}$ of data analysed. To determine the |
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trigger efficiency ``tag-and-probe'' method~\ref{TP} will be used. |
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|
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\item {\it Reconstruction}: we assign 2\% systematic uncertainty per |
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lepton due to initial tracker alignment which is of paramount |
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importance to reconstruct leptons, 2\% and 1\% is assigned for the |
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determination of the charge of the electron and muon candidates, |
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respectively. We assigned a larger electron charge identification |
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uncertainty due to much stronger Bremsstrahlung energy loss which |
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makes the charge identification more difficult. The mismeasurement of |
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the charge is of the order of 2\% in CMSSW\_1\_6\_7 release for |
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electron. The estimation of the fraction with data will be done by |
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looking at the \Z peak without opposite charge requirement. Then |
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number of events within the \Z mass windows asking for two leptons of |
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same sign will give us a estimate of the fraction of mismeasure sign |
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leptons. |
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|
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\item {\it Lepton identification}: we assign 4\% of systematic uncertainty |
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due to efficiency measurement from early data using ``tag-and-probe'' |
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method and 2\% for that for a muon. Additionally we assign a systematic |
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uncertainty on lepton energy scale of 2\% per lepton. |
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\item {\it Lepton identification}: we assign 4\% of systematic |
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uncertainty due to efficiency measurement from early data using |
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``tag-and-probe'' method and 2\% for that for a muon. Additionally we |
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assign a systematic uncertainty on lepton energy scale of 2\% per |
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lepton. The leptons scale will be established using the \Z mass peak. |
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|
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\item {\it PDF uncertainties}: we estimate PDF uncertainties following prescription |
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described in~\cite{OldNote}. The uncertainty is found to be |
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\end{center} |
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\caption{Systematic uncertainties for $pp\rightarrow \WZ$ cross section measurement |
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and significance estimation for 1 fb$^-1$ of integrated luminosity.} |
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and significance estimation for 300 \invpb of integrated luminosity.} |
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\label{tab:sys} |
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\end{table} |
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|
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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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%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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If we consider an error of 4\% |
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on the fake rate and an error of 1\% |
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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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\Delta N_j ^{t} = \sqrt{\left(\frac{p\left(N_t - pN_l\right)}{\left(\epsilon -p\right)^2}\right)^2 \times \Delta \epsilon^2 |
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+\left(\frac{\epsilon\left(\epsilon N_{l}-N_{t}\right)}{\left(\epsilon -p\right)^2}\right)^2 \times \Delta p^2 |
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+ \frac{p^2\left(\epsilon^2\Delta N_{l}^2 - \Delta N_{t}^2\left(2\epsilon -1\right)\right)}{\left(\epsilon -p\right)^2}} |
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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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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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%The overall error from the background substraction is XXX %18\%. |
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|
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\subsection{Summary of Systematics} |
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|
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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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\caption{Systematics per channels in percent for $pp\rightarrow WZ$ cross section measurement and significance estimation for 300 \invpb 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} |
