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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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conservatives. |
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conservative. |
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\subsection{Experimental Systematics} |
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\subsection{Background Substraction Systematics} |
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Two methods will be used to substract the different background. The |
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main background is the production $Z+jets$. Such background can be |
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estimated using data as presented in section~\ref{sec:SignalExt}. For |
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the $t\bar{t}$ background, we can use safely the side band around the |
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$Z$ mass in order to evaluate it. |
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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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If we consider an error of xx\% on the fake rate and an error of xx\% |
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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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From the fit, we will consider a systematics error of 10\%. |
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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} = \frac{\sqrt{(p[N_{t} - p(N_{l}+N_{t})])^2 \times \Delta \epsilon^2 |
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+(\epsilon[\epsilon(N_{l}+N_{t})-N_{t}]^2 \times \Delta p^2 |
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+ (p\epsilon)^2 \times N_{l} + [p(\epsilon -1 )]^2 \times N_{t}}}{\epsilon - p} |
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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 $N_{t}$ and $N_{l}$ represents respectivement the number of |
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events in the tight sample and in the loose sample and if they are |
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greater than 25.$\epsilon$ represent efficiency for a loose electron |
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to pass the tight criteria, $\Delta \epsilon$ the error on this |
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value.$p$ gives the probability for a fake loose electron to pass also |
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the tight criteria and $\Delta p$ its error. |
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An example of the method is given on figure~\ref{fig:Fitbkg}. The |
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number of estimated background compare to the true value is shown on |
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table~\ref{tab:FitbkgSub}. |
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We assign a systematics error of 20\%. |
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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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The overall error from the background substraction is 18\%. |
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\subsection{Summary of Systematics} |
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\label{tab:FullSys} |
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\end{table} |
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\subsection{Background Substraction} |
