| 1 |
< |
In this section, we will assign systematics errors to this |
| 2 |
< |
analysis. The assignement of systematics is expected to be |
| 3 |
< |
conservatives. |
| 4 |
< |
|
| 5 |
< |
\subsection{Experimental Systematics} |
| 6 |
< |
|
| 7 |
< |
The experimental systematics errors expected that will affect the |
| 8 |
< |
signal and standard model background are: |
| 1 |
> |
\section{Systematic uncertainties} |
| 2 |
> |
\label{sec:systematic} |
| 3 |
> |
In this section, we estimate systematics uncertainties of the methods |
| 4 |
> |
used in this analysis. We follow the rule of making conservative estimates |
| 5 |
> |
throughout this section. |
| 6 |
> |
|
| 7 |
> |
The sources of systematic uncertainties due to modeling of trigger, |
| 8 |
> |
reconstruction, PDF, and luminosity are described below |
| 9 |
> |
|
| 10 |
|
\begin{itemize} |
| 11 |
< |
\item For trigger selection, a systematics of 1\% is assigned. Even |
| 12 |
< |
though the efficiency of the signal is greater than 99\%, the trigger |
| 13 |
< |
path used for both muons and electron expect the leptons to be |
| 14 |
< |
isolated. As the isolation depends on the occupancy of the events, |
| 15 |
< |
the alignment of the tracker (when considering tracker isolation |
| 16 |
< |
variables) and noise in the calorimeters (when considering a |
| 17 |
< |
calorimetric isolation), this value is expected to be conservative. |
| 18 |
< |
|
| 19 |
< |
\item 2\% error is assigned on electron/muons reconstruction. Both of |
| 20 |
< |
them are link to alignment of the track in order to reconstruct the |
| 21 |
< |
leptons. A systematics of 2\% is assigned for the determination of |
| 22 |
< |
the charge of the electron candidate while 1\% for the muon as the |
| 23 |
< |
electron problem is coming from the high probability of emission of |
| 24 |
< |
photons. |
| 11 |
> |
\item {\it Trigger}: the trigger path used to select four categories |
| 12 |
> |
require leptons to be isolated. Though, the isolation criteria |
| 13 |
> |
depends on the occupancy of the sub-detectors, the alignment of the |
| 14 |
> |
tracker (when considering tracker isolation variables), and noise in |
| 15 |
> |
the calorimeters (when considering a calorimetric isolation), the |
| 16 |
> |
trigger efficiency is expected to be around 99\%, and therefore, a |
| 17 |
> |
systematic uncertainty is conservatively estimated as 1\%. From the |
| 18 |
> |
current analysis of $Z\rightarrow l^+l^-$ in |
| 19 |
> |
CMS~\cite{Zmumu}~\cite{Zee}, the number of \Z events is estimated of the |
| 20 |
> |
order of 50k per 100 pb$^{-1}$ of data analyzed. To determine the |
| 21 |
> |
trigger efficiency ``tag-and-probe'' method~\cite{TP} will be used. |
| 22 |
> |
|
| 23 |
> |
\item {\it Reconstruction}: we assign 2\% systematic uncertainty per |
| 24 |
> |
lepton due to initial tracker alignment which is of paramount |
| 25 |
> |
importance to reconstruct leptons, 2\% and 1\% is assigned for the |
| 26 |
> |
determination of the charge of the electron and muon candidates, |
| 27 |
> |
respectively. We assigned a larger electron charge identification |
| 28 |
> |
uncertainty due to much stronger Bremsstrahlung energy loss which |
| 29 |
> |
makes the charge identification more difficult. The mis-measurement of |
| 30 |
> |
the charge is of the order of 2\% in CMSSW\_1\_6\_7 release for |
| 31 |
> |
electron. The estimation of the fraction with data will be done by |
| 32 |
> |
looking at the \Z peak without opposite charge requirement. Then |
| 33 |
> |
number of events within the \Z mass windows asking for two leptons of |
| 34 |
> |
same sign will give us a estimate of the fraction of mis-measured sign |
| 35 |
> |
leptons. |
| 36 |
> |
|
| 37 |
> |
\item {\it Lepton identification}: we assign 4\% of systematic |
| 38 |
> |
uncertainty due to efficiency measurement from early data using |
| 39 |
> |
``tag-and-probe'' method and 2\% for that for a muon. Additionally we |
| 40 |
> |
assign a systematic uncertainty on lepton energy scale of 2\% per |
| 41 |
> |
lepton. The leptons scale will be established using the \Z mass peak. |
| 42 |
> |
|
| 43 |
> |
\item {\it PDF uncertainties}: we estimate PDF uncertainties following prescription |
| 44 |
> |
described in~\cite{OldNote}. The uncertainty is found to be |
| 45 |
> |
$$ \Delta \sigma_+ ^{tot} = 3.9\% \hspace{0.9cm} \Delta \sigma_- ^{tot} = 3.5\% $$ |
| 46 |
|
|
| 47 |
< |
\item A systematics of 1\% will be assigned for the measurement of |
| 26 |
< |
the lepton energy. |
| 27 |
< |
|
| 28 |
< |
\item 4\% of systematics are considered for the electron |
| 29 |
< |
identification, 2\% for the muon case. |
| 47 |
> |
\item {\it Luminosity}: we estimate luminosity uncertainty of 10\%. |
| 48 |
|
\end{itemize} |
| 49 |
|
|
| 50 |
< |
The PDF uncertainties on the signal has been determined in~\cite{OldNote}. |
| 33 |
< |
The uncertainty was found to be: |
| 34 |
< |
\begin{equation} |
| 35 |
< |
\Delta \sigma_+ ^{tot} = 3.9\% \hspace{0.9cm} \Delta \sigma_- ^{tot} = 3.5\% |
| 36 |
< |
\end{equation} |
| 37 |
< |
|
| 38 |
< |
The luminosity error is expected to be 10\%. |
| 39 |
< |
|
| 40 |
< |
The table~\ref{tab:sys} resume all systematics considered. |
| 50 |
> |
The systematic uncertainties are summarized in Table~\ref{tab:sys}. |
| 51 |
|
|
| 52 |
|
\begin{table}[!tb] |
| 53 |
|
\begin{center} |
| 54 |
< |
\begin{tabular}{|l|c|c|} \hline |
| 55 |
< |
Systematics Source (in \%) & Cross Section & Signficance \\ \hline |
| 56 |
< |
Luminosity & 10.0 & - \\ |
| 57 |
< |
Trigger & 1.0 & 1.0\\ |
| 58 |
< |
Lepton Reconstruction & 2.0 & 2.0\\ |
| 59 |
< |
Electron Charge Determination &2.0& 2.0\\ |
| 60 |
< |
Muon Charge Determination &1.0& 1.0\\ |
| 61 |
< |
Lepton Energy Scale& 1.0& 1.0\\ |
| 62 |
< |
Electron Identification& 4.0 &4.0\\ |
| 63 |
< |
Muon Identification& 2.0 &2.0\\ |
| 64 |
< |
PDF Uncertainties& - & + 3.9\\ |
| 65 |
< |
& & - 3.5 \\ \hline |
| 54 |
> |
\begin{tabular}{|l|c|} \hline |
| 55 |
> |
Source & Systematic uncertainty,\% \\ \hline |
| 56 |
> |
Luminosity & 10.0 \\ |
| 57 |
> |
Trigger & 1.0 \\ |
| 58 |
> |
Lepton reconstruction & 2.0 \\ |
| 59 |
> |
Electron charge determination & 2.0 \\ |
| 60 |
> |
Muon charge determination & 1.0 \\ |
| 61 |
> |
Lepton energy scale & 1.0 \\ |
| 62 |
> |
Electron identification & 4.0 \\ |
| 63 |
> |
Muon identification & 2.0 \\ |
| 64 |
> |
PDF uncertainties & 4.0 \\ |
| 65 |
> |
$M_{T}(W)$ requirement & 10.0 \\ \hline |
| 66 |
> |
|
| 67 |
|
\end{tabular} |
| 68 |
|
|
| 69 |
|
\end{center} |
| 70 |
< |
\caption{Systematics in percent for $pp\rightarrow WZ$ cross section measurement and significance estimation for 1 fb$^-1$ of integrated luminosity.} |
| 70 |
> |
\caption{Systematic uncertainties for $pp\rightarrow \WZ$ process |
| 71 |
> |
estimated for a scenario of 300~\invpb of integrated luminosity data sample.} |
| 72 |
|
\label{tab:sys} |
| 73 |
|
\end{table} |
| 74 |
|
|
| 75 |
|
|
| 76 |
< |
\subsection{Background Substraction Systematics} |
| 76 |
> |
We assign 100\% systematic uncertainty on the instrumental backgrounds without |
| 77 |
> |
genuine \Z boson. This correspond to 7\% effective systematic uncertainty on the final result. |
| 78 |
|
|
| 79 |
< |
Two methods will be used to substract the different background. The |
| 80 |
< |
main background is the production $Z+jets$. Such background can be |
| 81 |
< |
estimated using data as presented in section~\ref{sec:SignalExt}. For |
| 69 |
< |
the $t\bar{t}$ background, we can use safely the side band around the |
| 70 |
< |
$Z$ mass in order to evaluate it. |
| 71 |
< |
|
| 72 |
< |
If we consider an error of xx\% on the fake rate and an error of xx\% |
| 73 |
< |
on the efficiency on signal to go from loose to tight criteria, we can |
| 74 |
< |
calculate the error on the estimated background as follow: |
| 79 |
> |
The systematic uncertainty on the number of the genuine \Z boson background |
| 80 |
> |
events $\Delta N_j^t$ estimated using the matrix method described in Section~\ref{sec:D0Matrix} |
| 81 |
> |
is calculated as |
| 82 |
|
\begin{equation} |
| 83 |
< |
\Delta N_j ^{t} = \frac{\sqrt{(p[N_{t} - p(N_{l}+N_{t})])^2 \times \Delta \epsilon^2 |
| 84 |
< |
+(\epsilon[\epsilon(N_{l}+N_{t})-N_{t}]^2 \times \Delta p^2 |
| 85 |
< |
+ (p\epsilon)^2 \times N_{l} + [p(\epsilon -1 )]^2 \times N_{t}}}{\epsilon - p} |
| 79 |
< |
%\Delta N_j ^{tight} = \frac{\sqrt{(p_{fake}[N_{tight} - p_{fake}(N_{loose}+N_{tight})])^2 \dot \Delta \epsilon^2 |
| 80 |
< |
%+(\epsilon[\epsilon(N_{loose}+N_{tight})-N_{tight}]^2 \dot \Delta p_{fake}^2 |
| 81 |
< |
%+ (p_{fake}\epsilon)^2 \dot N_{loose} + [p_{fake}(\epsilon -1 )]^2 \dot N_{tight}}}{\epsilon_{tight} - p_{fake}} |
| 83 |
> |
\left(\Delta N_j ^{t}\right)^2 = \left(\frac{p\left(N_t - pN_l\right)}{\left(\epsilon -p\right)^2}\right)^2 \Delta \epsilon^2 |
| 84 |
> |
+\left(\frac{\epsilon\left(\epsilon N_{l}-N_{t}\right)}{\left(\epsilon -p\right)^2}\right)^2 \Delta p^2 |
| 85 |
> |
+ \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}, |
| 86 |
|
\end{equation} |
| 83 |
– |
where $N_{t}$ and $N_{l}$ represents respectivement the number of |
| 84 |
– |
events in the tight sample and in the loose sample and if they are |
| 85 |
– |
greater than 25.$\epsilon$ represent efficiency for a loose electron |
| 86 |
– |
to pass the tight criteria, $\Delta \epsilon$ the error on this |
| 87 |
– |
value.$p$ gives the probability for a fake loose electron to pass also |
| 88 |
– |
the tight criteria and $\Delta p$ its error. |
| 87 |
|
|
| 88 |
< |
|
| 89 |
< |
|
| 90 |
< |
An example of the method is given on figure~\ref{fig:Fitbkg}. The |
| 91 |
< |
number of estimated background compare to the true value is shown on |
| 92 |
< |
table~\ref{tab:FitbkgSub}. |
| 93 |
< |
|
| 94 |
< |
We assign a systematics error of 20\%. |
| 95 |
< |
|
| 96 |
< |
|
| 97 |
< |
\subsection{Summary of Systematics} |
| 98 |
< |
|
| 99 |
< |
In table~\ref{tab:FullSys}, the systematics errors are expressed for |
| 102 |
< |
each channels. |
| 88 |
> |
where $N_t$ and $N_l$ are the numbers of observed events in tight and loose samples |
| 89 |
> |
after the \ZZ and \Z$\gamma$ backgrounds have been subtracted. $\Delta N_t$ and $\Delta N_l$ |
| 90 |
> |
are the systematic uncertainties associated with this subtraction. We take those as |
| 91 |
> |
100\% of the estimated physics background from the Monte Carlo simulation. Finally, |
| 92 |
> |
$\epsilon$ and $p$ are genuine and misidentified ``loose'' lepton efficiency to |
| 93 |
> |
satisfy ``tight'' requirements. |
| 94 |
> |
|
| 95 |
> |
We summarize full systematic uncertainties in Table~\ref{tab:FullSys} for each |
| 96 |
> |
individual signature. The systematic uncertainty is smaller than statistical uncertainty |
| 97 |
> |
which is roughly 30\% for each channel. Improvement in understanding of the MET, |
| 98 |
> |
better measurement of the $p_{fake}$ allow to decrease the overall systematic uncertainty |
| 99 |
> |
with larger data sample. |
| 100 |
|
|
| 101 |
|
\begin{table}[!tb] |
| 102 |
|
\begin{center} |
| 103 |
< |
\begin{tabular}{|l|c|c|} \hline |
| 104 |
< |
Channels & Cross Section & Signficance \\ \hline |
| 105 |
< |
3e & 8.4\% +10\% = 13.1\% & +9.3\% / - 9.2\% \\ |
| 106 |
< |
2e1$\mu$ & 7.7\% +10\% = 12.6\% & +8.7\% / - 8.5\% \\ |
| 107 |
< |
1e2$\mu$ & 6.5\% +10\% = 11.9\% & +7.6\% / - 7.4\% \\ |
| 108 |
< |
3$\mu$ & 5.5\% +10\% = 11.4\% & +6.7\% / - 6.5\% \\\hline |
| 103 |
> |
\begin{tabular}{|l|c|c|c|} \hline |
| 104 |
> |
Channels & Modeling, \% & Background estimation, \% & Total, \% \\ \hline |
| 105 |
> |
$3e$ & 17 & 13 & 21 \\ |
| 106 |
> |
$2e1\mu$ & 17 & 11 & 20 \\ |
| 107 |
> |
$2\mu1e$ & 16 & 15 & 22 \\ |
| 108 |
> |
$3\mu$ & 16 & 10 & 19 \\ \hline |
| 109 |
|
\end{tabular} |
| 110 |
|
|
| 111 |
|
\end{center} |
| 112 |
< |
\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.} |
| 112 |
> |
\caption{Total systematic uncertainty for identification of $pp\rightarrow WZ$ production.} |
| 113 |
|
\label{tab:FullSys} |
| 114 |
|
\end{table} |
| 115 |
|
|
| 119 |
– |
|
| 120 |
– |
|
