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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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\subsection{Experimental Systematics}
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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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\item 3\% 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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\item A systematics of 1\% will be assigned for the measurement of
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the lepton energy.
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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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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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beaucero |
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\Delta \sigma_+ ^{tot} = 3.9\% \hspace{0.9cm} \Delta \sigma_- ^{tot} = 3.5\%
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beaucero |
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\end{equation}
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The luminosity error is expected to be 10\%.
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The table~\ref{tab:sys} resume all systematics considered.
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\begin{table}[!]
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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 & 3.0 & 3.0\\
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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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\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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\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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beaucero |
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If we consider an error of xx\% on the fake rate and an error of xx\%
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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_{t} - p}
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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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