| 4 |
|
used in this analysis. We follow the rule of making conservative estimates |
| 5 |
|
throughout this section. |
| 6 |
|
|
| 7 |
– |
\subsection{Modeling systematics} |
| 8 |
– |
|
| 7 |
|
The sources of systematic uncertainties due to modeling of trigger, |
| 8 |
|
reconstruction, PDF, and luminosity are described below |
| 9 |
|
|
| 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~\ref{Zmumu}~\ref{Zee}, the number of \Z events is estimated of the |
| 20 |
< |
order of 50k per 100 pb$^{-1}$ of data analysed. To determine the |
| 21 |
< |
trigger efficiency ``tag-and-probe'' method~\ref{TP} will be used. |
| 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 |
| 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 mismeasurement of |
| 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 mismeasure sign |
| 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 |
| 42 |
|
|
| 43 |
|
\item {\it PDF uncertainties}: we estimate PDF uncertainties following prescription |
| 44 |
|
described in~\cite{OldNote}. The uncertainty is found to be |
| 45 |
< |
$$ \Delta \sigma_+ ^{tot} = 3.9\% \hspace{0.9cm} \Delta \sigma_- ^{tot} = 3.5\% $$. |
| 45 |
> |
$$ \Delta \sigma_+ ^{tot} = 3.9\% \hspace{0.9cm} \Delta \sigma_- ^{tot} = 3.5\% $$ |
| 46 |
|
|
| 47 |
|
\item {\it Luminosity}: we estimate luminosity uncertainty of 10\%. |
| 48 |
|
\end{itemize} |
| 51 |
|
|
| 52 |
|
\begin{table}[!tb] |
| 53 |
|
\begin{center} |
| 54 |
< |
\begin{tabular}{|l|c|c|} \hline |
| 55 |
< |
& \multicolumn{2}{c|}{Systematic uncertainty} \\ |
| 56 |
< |
Source & on the cross section,\% & on the signficance,\% \\ \hline |
| 57 |
< |
Luminosity & 10.0 & - \\ |
| 58 |
< |
Trigger & 1.0 & 1.0\\ |
| 59 |
< |
Lepton reconstruction & 2.0 & 2.0\\ |
| 60 |
< |
Electron charge determination &2.0& 2.0\\ |
| 61 |
< |
Muon charge determination &1.0& 1.0\\ |
| 62 |
< |
Lepton energy scale& 1.0& 1.0\\ |
| 63 |
< |
Electron identification& 4.0 &4.0\\ |
| 64 |
< |
Muon identification& 2.0 &2.0\\ |
| 65 |
< |
PDF uncertainties& - & + 3.9\\ |
| 66 |
< |
& & - 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{Systematic uncertainties for $pp\rightarrow \WZ$ cross section measurement |
| 71 |
< |
and significance estimation for 300 \invpb 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{Systematic uncertainties due to background estimation method} |
| 77 |
< |
|
| 80 |
< |
In the following we estimate a systematic uncertainty due to estimation |
| 81 |
< |
of background using the matrix method described in Section~\ref{sec:D0Matrix} above. |
| 82 |
< |
|
| 83 |
< |
|
| 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 |
< |
We present here, the result for the case where the $W$ is decaying via |
| 80 |
< |
an electron. |
| 81 |
< |
|
| 88 |
< |
Two steps will be used to substract the different background: first, |
| 89 |
< |
the non peaking background should be substracted, then the background |
| 90 |
< |
$Z+jets$ will be determine using the method described |
| 91 |
< |
in~\ref{sec:D0Matrix}. |
| 92 |
< |
|
| 93 |
< |
%From the fit, we will consider a systematics error of 10\%. |
| 94 |
< |
|
| 95 |
< |
If we consider an error of 4\% |
| 96 |
< |
on the fake rate and an error of 1\% |
| 97 |
< |
on the efficiency on signal to go from loose to tight criteria, we can |
| 98 |
< |
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} = \sqrt{\left(\frac{p\left(N_t - pN_l\right)}{\left(\epsilon -p\right)^2}\right)^2 \times \Delta \epsilon^2 |
| 84 |
< |
+\left(\frac{\epsilon\left(\epsilon N_{l}-N_{t}\right)}{\left(\epsilon -p\right)^2}\right)^2 \times \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}} |
| 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} |
| 104 |
– |
where $N_{t}$,$\Delta N_{t}$ and $N_{l}$,$\Delta N_{l}$ represents |
| 105 |
– |
respectivement the number of events in the tight sample and in the |
| 106 |
– |
loose sample and their errors.$\epsilon$ represent efficiency for a |
| 107 |
– |
loose electron to pass the tight criteria, $\Delta \epsilon$ the error |
| 108 |
– |
on this value.$p$ gives the probability for a fake loose electron to |
| 109 |
– |
pass also the tight criteria and $\Delta p$ its error. |
| 110 |
– |
|
| 111 |
– |
%The overall error from the background substraction is XXX %18\%. |
| 112 |
– |
|
| 113 |
– |
\subsection{Summary of Systematics} |
| 87 |
|
|
| 88 |
< |
In table~\ref{tab:FullSys}, the systematics errors are expressed for |
| 89 |
< |
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 300 \invpb 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 |
|
|
