Notes/WZCSA07/Sys.tex

\section{Systematic uncertainties}
\label{sec:systematic}
In this section, we estimate systematics uncertainties of the methods
used in this analysis. We follow the rule of making conservative estimates
throughout this section.

The sources of systematic uncertainties due to modeling of trigger,
reconstruction, PDF, and luminosity are described below
 
\begin{itemize}
 \item {\it Trigger}: the trigger path used to select four categories
 require leptons to be isolated. Though, the isolation criteria
 depends on the occupancy of the sub-detectors, the alignment of the
 tracker (when considering tracker isolation variables), and noise in
 the calorimeters (when considering a calorimetric isolation), the
 trigger efficiency is expected to be around 99\%, and therefore, a
 systematic uncertainty is conservatively estimated as 1\%. From the
 current analysis of $Z\rightarrow l^+l^-$ in
 CMS~\cite{Zmumu}~\cite{Zee}, the number of \Z events is estimated of the
 order of 50k per 100 pb$^{-1}$ of data analyzed. To determine the
 trigger efficiency ``tag-and-probe'' method~\cite{TP} will be used.

 \item {\it Reconstruction}: we assign 2\% systematic uncertainty per
 lepton due to initial tracker alignment which is of paramount
 importance to reconstruct leptons, 2\% and 1\% is assigned for the
 determination of the charge of the electron and muon candidates,
 respectively. We assigned a larger electron charge identification
 uncertainty due to much stronger Bremsstrahlung energy loss which
 makes the charge identification more difficult. The mis-measurement of
 the charge is of the order of 2\% in CMSSW\_1\_6\_7 release for
 electron. The estimation of the fraction with data will be done by
 looking at the \Z peak without opposite charge requirement. Then
 number of events within the \Z mass windows asking for two leptons of
 same sign will give us a estimate of the fraction of mis-measured sign
 leptons.
  
 \item {\it Lepton identification}: we assign 4\% of systematic
 uncertainty due to efficiency measurement from early data using
 ``tag-and-probe'' method and 2\% for that for a muon. Additionally we
 assign a systematic uncertainty on lepton energy scale of 2\% per
 lepton. The leptons scale will be established using the \Z mass peak.

\item {\it PDF uncertainties}: we estimate PDF uncertainties following prescription
described in~\cite{OldNote}. The uncertainty is found to be
$$ \Delta \sigma_+ ^{tot} = 3.9\% \hspace{0.9cm} \Delta \sigma_- ^{tot} = 3.5\% $$

\item {\it Luminosity}: we estimate luminosity uncertainty of 10\%.
\end{itemize}

The systematic uncertainties are summarized in Table~\ref{tab:sys}.

\begin{table}[!tb]
\begin{center}
\begin{tabular}{|l|c|} \hline
Source   &   Systematic uncertainty,\% \\ \hline 
Luminosity                      &   10.0        \\
Trigger                         &    1.0        \\
Lepton reconstruction           &    2.0        \\
Electron charge determination   &    2.0        \\
Muon charge determination       &    1.0        \\
Lepton energy scale             &    1.0        \\
Electron identification         &    4.0        \\
Muon identification             &    2.0        \\
PDF uncertainties               &    4.0        \\
$M_{T}(W)$ requirement          &   10.0        \\ \hline

\end{tabular}

\end{center}
\caption{Systematic uncertainties for $pp\rightarrow \WZ$ process
estimated for a scenario of 300~\invpb of integrated luminosity data sample.}
\label{tab:sys}
\end{table}


We assign 100\% systematic uncertainty on the instrumental backgrounds without 
genuine \Z boson. This correspond to 7\% effective systematic uncertainty on the final result.

The systematic uncertainty on the number of the genuine \Z boson background
events $\Delta N_j^t$ estimated using the matrix method described in Section~\ref{sec:D0Matrix}
is calculated as
\begin{equation}
\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 
+\left(\frac{\epsilon\left(\epsilon N_{l}-N_{t}\right)}{\left(\epsilon -p\right)^2}\right)^2 \Delta p^2 
+ \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},
\end{equation}

where $N_t$ and $N_l$ are the numbers of observed events in tight and loose samples
after the \ZZ and \Z$\gamma$ backgrounds have been subtracted. $\Delta N_t$ and $\Delta N_l$ 
are the systematic uncertainties associated with this subtraction.  We take those as
100\% of the estimated physics background from the Monte Carlo simulation. Finally,
$\epsilon$ and $p$ are genuine and misidentified ``loose'' lepton efficiency to
satisfy ``tight'' requirements.

We summarize full systematic uncertainties in Table~\ref{tab:FullSys} for each
individual signature. The systematic uncertainty is comparable to the statistical
uncertainty which is roughly 30\% for each channel. Improvement in understanding
of the physics and instrumental backgrounds without genuine \Z bosons, that are 
currently subtracted with overly conservative 100\%, as well as
understanding of the MET, better measurement of the $p_{fake}$ will 
allow to decrease the overall systematic uncertainty with real data.

\begin{table}[!tb]
\begin{center}
\begin{tabular}{|l|c|c|c|} \hline
Channels        &  Modeling, \% &  Background estimation, \%    & Total, \%     \\ \hline 
$3e$            &  21           &  27                           & 34            \\ 
$2e1\mu$        &  19           &  16                           & 25            \\ 
$2\mu1e$        &  17           &  31                           & 35            \\ 
$3\mu$          &  17           &  12                           & 21            \\ \hline 
\end{tabular}

\end{center}
\caption{Total systematic uncertainty for identification of $pp\rightarrow WZ$ production.}
\label{tab:FullSys}
\end{table}

Revision:	1.21
Committed:	Tue Aug 12 19:24:08 2008 UTC (16 years, 8 months ago) by ymaravin
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#	User	Rev	Content
1	ymaravin	1.14	\section{Systematic uncertainties}
2			\label{sec:systematic}
3	ymaravin	1.7	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	beaucero	1.2	\begin{itemize}
11	beaucero	1.12	\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	beaucero	1.16	CMS~\cite{Zmumu}~\cite{Zee}, the number of \Z events is estimated of the
20	ymaravin	1.20	order of 50k per 100 pb$^{-1}$ of data analyzed. To determine the
21	beaucero	1.16	trigger efficiency ``tag-and-probe'' method~\cite{TP} will be used.
22	beaucero	1.12
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	ymaravin	1.20	makes the charge identification more difficult. The mis-measurement of
30	beaucero	1.12	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	ymaravin	1.20	same sign will give us a estimate of the fraction of mis-measured sign
35	beaucero	1.12	leptons.
36	ymaravin	1.7
37	beaucero	1.12	\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	beaucero	1.15	lepton. The leptons scale will be established using the \Z mass peak.
42	ymaravin	1.7
43			\item {\it PDF uncertainties}: we estimate PDF uncertainties following prescription
44			described in~\cite{OldNote}. The uncertainty is found to be
45	beaucero	1.17	$$ \Delta \sigma_+ ^{tot} = 3.9\% \hspace{0.9cm} \Delta \sigma_- ^{tot} = 3.5\% $$
46	beaucero	1.2
47	ymaravin	1.7	\item {\it Luminosity}: we estimate luminosity uncertainty of 10\%.
48	beaucero	1.2	\end{itemize}
49
50	ymaravin	1.7	The systematic uncertainties are summarized in Table~\ref{tab:sys}.
51	beaucero	1.2
52	beaucero	1.4	\begin{table}[!tb]
53	beaucero	1.2	\begin{center}
54	ymaravin	1.20	\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	beaucero	1.2	\end{tabular}
68
69			\end{center}
70	ymaravin	1.20	\caption{Systematic uncertainties for $pp\rightarrow \WZ$ process
71			estimated for a scenario of 300~\invpb of integrated luminosity data sample.}
72	beaucero	1.2	\label{tab:sys}
73			\end{table}
74
75
76	ymaravin	1.20	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	beaucero	1.2
79	ymaravin	1.20	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	beaucero	1.3	\begin{equation}
83	ymaravin	1.20	\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	beaucero	1.3	\end{equation}
87	beaucero	1.4
88	ymaravin	1.20	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	ymaravin	1.21	individual signature. The systematic uncertainty is comparable to the statistical
97			uncertainty which is roughly 30\% for each channel. Improvement in understanding
98			of the physics and instrumental backgrounds without genuine \Z bosons, that are
99			currently subtracted with overly conservative 100\%, as well as
100			understanding of the MET, better measurement of the $p_{fake}$ will
101			allow to decrease the overall systematic uncertainty with real data.
102	beaucero	1.4
103			\begin{table}[!tb]
104			\begin{center}
105	ymaravin	1.20	\begin{tabular}{\|l\|c\|c\|c\|} \hline
106			Channels & Modeling, \% & Background estimation, \% & Total, \% \\ \hline
107	ymaravin	1.21	$3e$ & 21 & 27 & 34 \\
108			$2e1\mu$ & 19 & 16 & 25 \\
109			$2\mu1e$ & 17 & 31 & 35 \\
110			$3\mu$ & 17 & 12 & 21 \\ \hline
111	beaucero	1.4	\end{tabular}
112
113			\end{center}
114	ymaravin	1.20	\caption{Total systematic uncertainty for identification of $pp\rightarrow WZ$ production.}
115	beaucero	1.4	\label{tab:FullSys}
116			\end{table}
117