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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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\subsection{Modeling systematics} |
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The sources of systematic uncertainties due to modeling of trigger, |
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reconstruction, PDF, and luminosity are described below |
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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 100pb$^{-1}$ 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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CMS~\cite{Zmumu}~\cite{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~\cite{TP} will be used. |
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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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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 letpons scale will be established using the \Z mass peak. |
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lepton. The leptons scale will be established using the \Z mass peak. |
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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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$$ \Delta \sigma_+ ^{tot} = 3.9\% \hspace{0.9cm} \Delta \sigma_- ^{tot} = 3.5\% $$. |
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$$ \Delta \sigma_+ ^{tot} = 3.9\% \hspace{0.9cm} \Delta \sigma_- ^{tot} = 3.5\% $$ |
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\item {\it Luminosity}: we estimate luminosity uncertainty of 10\%. |
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\end{itemize} |
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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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PDF uncertainties& + 3.9 & + 3.9\\ |
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&- 3.5 & - 3.5 \\ |
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$M_{T}(W)$ requirement & 10 & 10 \\ \hline |
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\end{tabular} |
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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 300 \invpb 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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$Z+jets$ will be determine using the method described |
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in~\ref{sec:D0Matrix}. |
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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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If we consider an error of 10\% |
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on the fake rate and an error of 2\% |
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If we consider an error $\Delta p$ |
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%of 4\% |
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on the fake rate and an error $\Delta \epsilon$ |
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%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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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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loose electron to pass the tight criteria. |
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%, $\Delta \epsilon$ the error on this value. |
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$p$ gives the probability for a fake loose electron to |
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pass also the tight criteria. |
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%and $\Delta p$ its error. |
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The overall error from the background substraction is XXX %18\%. |
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%The overall error from the background substraction is XXX %18\%. |
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\subsection{Summary of Systematics} |
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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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3e & +9.3\% / - 9.2\% +10\% = +13.7\% / -13.6\% & +9.3\% / - 9.2\% \\ |
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2e1$\mu$ & +8.7\% / - 8.5\% +10\% = +13.3\% / -13.1\% & +8.7\% / - 8.5\% \\ |
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1e2$\mu$ & +7.6\% / - 7.4\% +10\% = +12.7\% / -12.4\% & +7.6\% / - 7.4\% \\ |
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3$\mu$ & +6.7\% / - 6.5\% +10\% = +12.0\% / -11.9\% & +6.7\% / - 6.5\% \\\hline |
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\end{tabular} |
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\end{center} |
