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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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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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> |
|
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> |
\subsection{Modeling systematics} |
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|
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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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|
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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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\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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> |
|
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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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|
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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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|
|
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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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> |
\item {\it Luminosity}: we estimate luminosity uncertainty of 10\%. |
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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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> |
The systematic uncertainties are summarized in Table~\ref{tab:sys}. |
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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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& \multicolumn{2}{c|}{Systematic uncertainty} \\ |
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Source & on the cross section,\% & on the 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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> |
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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|
|
| 58 |
|
\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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\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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|
\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} |
| 65 |
> |
\subsection{Systematic uncertainties due to background estimation method} |
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|
| 67 |
> |
In the following we estimate a systematic uncertainty due to estimation |
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> |
of background using the matrix method described in Section~\ref{sec:D0Matrix} above. |
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> |
|
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> |
|
| 71 |
|
|
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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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|
|
| 80 |
|
From the fit, we will consider a systematics error of 10\%. |
| 81 |
|
|
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< |
If we consider an error of 5\% on the fake rate and an error of 2\% |
| 82 |
> |
If we consider an error of 10\% |
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> |
on the fake rate and an error of 2\% |
| 84 |
|
on the efficiency on signal to go from loose to tight criteria, we can |
| 85 |
|
calculate the error on the estimated background as follow: |
| 86 |
|
\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}} |
| 87 |
> |
\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 |
| 88 |
> |
+\left(\frac{\epsilon\left(\epsilon N_{l}-N_{t}\right)}{\left(\epsilon -p\right)^2}\right)^2 \times \Delta p^2 |
| 89 |
> |
+ \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}} |
| 90 |
|
\end{equation} |
| 91 |
|
where $N_{t}$,$\Delta N_{t}$ and $N_{l}$,$\Delta N_{l}$ represents |
| 92 |
|
respectivement the number of events in the tight sample and in the |
| 95 |
|
on this value.$p$ gives the probability for a fake loose electron to |
| 96 |
|
pass also the tight criteria and $\Delta p$ its error. |
| 97 |
|
|
| 98 |
< |
The overall error from the background substraction is 18\%. |
| 98 |
> |
The overall error from the background substraction is XXX %18\%. |
| 99 |
|
|
| 100 |
|
\subsection{Summary of Systematics} |
| 101 |
|
|
| 117 |
|
\label{tab:FullSys} |
| 118 |
|
\end{table} |
| 119 |
|
|
| 116 |
– |
\subsection{Background Substraction} |
