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version 1.1, 2011/05/18 21:30:39
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version 1.2, 2011/06/01 01:20:54
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| \newpage |
\newpage |
| \section{Systematic uncertainties} |
\section{Systematic uncertainties} |
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| Several factors contribute to systematic uncertainties in the measurement. Here we describe such uncertainties. |
The following components are added in quadrature to estimate the total systematic uncertainty. |
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| \subsection{JES} |
\subsection{Jet Energy Scale} |
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| \noindent The jet energy scale (JES) systematic is determined by shifiting the jet energy scale |
\noindent The jet energy scale (JES) systematic is determined by shifiting the jet energy scale |
| by $\pm 1 \sigma$ in all MC samples. |
by $\pm 1 \sigma$ in all MC samples. |
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| \subsection{TES} |
\subsection{Tau Energy Scale} |
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| \noindent The tau energy scale (TES) systematic is determined by shifiting the tau energy scale |
\noindent The tau energy scale (TES) systematic is determined by shifiting the tau energy scale |
| by its uncertainty as given in \cite{tes_sys}. |
by its uncertainty as given in \cite{tes_sys}. |
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Line 21 by its uncertainty as given in \cite{tes
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Line 21 by its uncertainty as given in \cite{tes
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| resolution by $\pm 1 \sigma$ in all MC samples. |
resolution by $\pm 1 \sigma$ in all MC samples. |
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| \subsection{Trigger} |
\subsection{Trigger} |
| \noindent Each event was corrected by the ratio of the actual and predicted trigger result as a function of $H_{T}$, which was |
\noindent For this systematics, the level of agreement (as a function of $H_T$) when applying the trigger |
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turn-on curves to 4-jet data events was measured. We then used the ratio between the predicted and the |
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actual trigger decision as a function of $H_T$ to assign a error due to the trigger modeling. All MC events |
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were re-weighted by this ratio as a function of $H_T$, which was |
| used based on the fact that the agreement varies as function of it. |
used based on the fact that the agreement varies as function of it. |
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Line 32 using different fragmentation functions.
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Line 35 using different fragmentation functions.
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| \subsection{\boldmath $b$-tagging} |
\subsection{\boldmath $b$-tagging} |
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| \noindent b-tagging uncertainty effects are taken into account by varying the |
\noindent b-tagging uncertainty effects are taken into account by varying the |
| systematic and statistical errors on the MC tagging weights. |
systematic and statistical uncertainties on the MC tagging weights. |
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| These errors (which are computed using standard D\O\ b ID group tools) arise form several independent sources \cite{bID-p20}: |
These uncertainties (which are computed using standard D0 b ID group tools) arise form several independent sources \cite{bID-p20}: |
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| \begin{itemize} |
\begin{itemize} |
| \item B-jet tagging parameterization. |
\item B-jet tagging parameterization. |
|
Line 44 These errors (which are computed using s
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Line 47 These errors (which are computed using s
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| %are derived from the statistical error due to finite MC statistics. |
%are derived from the statistical error due to finite MC statistics. |
| \item Semi-leptonic b-tagging efficiency parameterization in MC and in data |
\item Semi-leptonic b-tagging efficiency parameterization in MC and in data |
| (System 8). |
(System 8). |
| \item Taggability. This includes the statistical error due to finite statistic |
\item Taggability. This includes the statistical uncertainty due to finite statistic |
| in the samples from which it had been derived and systematic, reflecting |
in the samples from which it had been derived and systematic, reflecting |
| the (neglected) taggability dependence on the jet multiplicity. |
the (neglected) taggability dependence on the jet multiplicity. |
| \end{itemize} |
\end{itemize} |
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| \subsection{\boldmath $\tau$ ID systematics} |
\subsection{\boldmath $\tau$ identification} |
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| \noindent Here we include systematics associated to the NN cut (NN $>$ 0.90 for taus types 1 and 2 and NN $>$ 0.95 for taus type 3) |
\noindent Here we include systematics associated to the NN cut (NN $>$ 0.90 for taus types 1 and 2 and NN $>$ 0.95 for taus type 3) |
| applied to select hadronic taus. As recommended by the $\tau $-ID group |
applied to select hadronic taus. As recommended by the $\tau $-ID group |
| these systematics are 9.5\%, 3.5\% and 5.0\% for taus type 1, 2 and 3 respectively. However in this analysis we chose |
these systematics are 9.5\%, 3.5\% and 5.0\% for taus type 1, 2 and 3 respectively. However in this analysis we chose |
| treat taus types 1 and 2 together. This led us to combine their uncertainties in the following way |
to treat taus types 1 and 2 together. This led us to combine their uncertainties in the following way |
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| \begin{center} |
\begin{center} |
| \begin{equation} |
\begin{equation} |
| sys_{12} = \displaystyle \sqrt{\epsilon_{1}^{2}*f_{1}^{2} + \epsilon_{2}^{2}*f_{2}^{2}} |
sys_{12} = \displaystyle \sqrt{\epsilon_{1}^{2} \cdot f_{1}^{2} + \epsilon_{2}^{2} \cdot f_{2}^{2}} |
| \end{equation} |
\end{equation} |
| \end{center} |
\end{center} |
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Line 67 sys_{12} = \displaystyle \sqrt{\epsilon_
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Line 70 sys_{12} = \displaystyle \sqrt{\epsilon_
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| $f_{1}$ and $f_{2}$ are the fractions of taus types 1 (0.16) and 2 (0.84) respectively. |
$f_{1}$ and $f_{2}$ are the fractions of taus types 1 (0.16) and 2 (0.84) respectively. |
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| \subsection{\label{sub:qcd_syst}QCD systematics} |
\subsection{\label{sub:qcd_syst}QCD modeling} |
| As explained in the section \ref{sub:Variables} we use the control (b-veto) data set to |
As explained in the section \ref{sub:Variables} we use the control (b-veto) sample to |
| validate our method of modeling the multijet background. Therefore we have to |
validate our method of modeling the multijet background. Therefore we have to |
| use the same sample to evaluate the associated uncertainties. The way it was |
use the same sample to evaluate the associated uncertainties. We did this |
| done is by reweighting topological event NN for QCD template |
by reweighting topological event NN for QCD template |
| (``loose-tight'' $\tau$), so that it matches the one for ``tight'' $\tau$ data exactly |
(``loose-tight'' $\tau$), so that it matches the one for ``tight'' $\tau$ data exactly |
| (electroweak beckgrounds were subtracted). |
(electroweak backgrounds were subtracted). |
| %Figure \ref{fig:qcd_reweight} shows that this scaling is close to 1, as it should be, since QCD template |
%Figure \ref{fig:qcd_reweight} shows that this scaling is close to 1, as it should be, since QCD template |
| %models the QCD-dominated data very well. |
%models the QCD-dominated data very well. |
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| \subsection{W and Z scale factors} |
\subsection{$W$ and $Z$ scale factors} |
| We apply a ascale factor of 1.47 to both W + bb and W + cc events with an uncertainty of 15\%. At the same time a scales factors |
We apply a scale factor of 1.47 to both $Wbb$ and $Wcc$ events with an uncertainty of 15\%. At the same time a scales factors |
| of 1.52 and 1.67 are applied to Z + bb and Z + cc events, both with an uncertainty of 20\%. |
of 1.52 and 1.67 are applied to $Zbb$ and $Zcc$ events, both with an uncertainty of 20\%. |
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| \subsection{Template statistics} |
\subsection{Template statistics} |
|
Line 90 varying the content of each bin of the Q
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Line 93 varying the content of each bin of the Q
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| how the cross section result changed. |
how the cross section result changed. |
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| \subsection{$t\bar{t}$ contamination in the loose-tight sample} |
\subsection{$t\bar{t}$ contamination in the loose-tight sample} |
| When measuring the cross-section we had to take into account the signal contamination in the loose-tight |
When measuring the cross section we had to take into account the signal contamination in the loose-tight |
| sample we use to model QCD in the high NN region. The systematic uncertainty in this case |
sample we use to model QCD in the high NN region. The systematic uncertainty in this case |
| is calculated by varying the final assumed cross section by $\pm 1 \sigma$, re-estimating the signal contamination |
is calculated by varying the final assumed cross section by $\pm 1 \sigma$, re-estimating the signal contamination |
| and finally measuring the up and down values of the cross section. |
and finally measuring the up and down values of the cross section. |
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Line 98 and finally measuring the up and down va
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Line 101 and finally measuring the up and down va
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| \subsection{PDF} |
\subsection{PDF} |
| Systematics on Parton Distribution Functions (PDF) are estimated by reweighting signal $t\bar{t}$ MC from |
Systematics on Parton Distribution Functions (PDF) are estimated by reweighting signal $t\bar{t}$ MC from |
| CTEQ6L1 to CTEQ6.1m and its twenty error PDF's. The reweighting of the PDF's is done by using {\tt caf\_pdfreweight} |
CTEQ6L1 to CTEQ6.1m and its twenty error PDF's. The reweighting of the PDF's is done by using {\tt caf\_pdfreweight} |
| package tool on Pythia $t\bar{t}$ MC. We then assigned the relative PDF uncertainty obtained with Pythia on the Alpgen |
package tool on {\sc PYTHIA} $t\bar{t}$ MC. We then assigned the relative PDF uncertainty obtained with {\sc PYTHIA} |
| $t\bar{t}$ MC. |
on the {\sc ALPGEN} $t\bar{t}$ MC. |
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| \subsection{Luminosity} |
\subsection{Luminosity} |
| Here we take the D\O\ standard measured uncertainty on luminosity of 6.1$\%$ . |
Here we take the D0 standard measured uncertainty on luminosity of 6.1$\%$ . |
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| Tables \ref{cap:Syst1} and \ref{cap:Syst2} summarize all of these uncertainty sources and shows how the resulting cross section shifts. |
Tables \ref{cap:Syst1} and \ref{cap:Syst2} summarize all of these uncertainty sources and shows how the resulting cross section shifts. |
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Line 186 Channel&
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Line 189 Channel&
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| {\footnotesize $_{+0.097, -0.084}$ }& |
{\footnotesize $_{+0.097, -0.084}$ }& |
| {\footnotesize $_{+0.188, -0.198}$ }& |
{\footnotesize $_{+0.188, -0.198}$ }& |
| {\footnotesize $_{+0.092, -0.081}$ }\\ |
{\footnotesize $_{+0.092, -0.081}$ }\\ |
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\hline |
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{\footnotesize TOTAL }& |
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{\footnotesize $_{+0.839, -0.791}$ }& |
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{\footnotesize $_{+0.882, -0.820}$ }& |
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{\footnotesize $_{+0.843, -0.779}$ }\\ |
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| \end{tabular}{\footnotesize \par} |
\end{tabular}{\footnotesize \par} |
| %\end{ruledtabular} |
%\end{ruledtabular} |
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Line 262 Channel&
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Line 270 Channel&
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| {\footnotesize $_{+0.097, -0.084}$ }& |
{\footnotesize $_{+0.097, -0.084}$ }& |
| {\footnotesize $_{+0.188, -0.198}$ }& |
{\footnotesize $_{+0.188, -0.198}$ }& |
| {\footnotesize $_{+0.092, -0.081}$ }\\ |
{\footnotesize $_{+0.092, -0.081}$ }\\ |
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\hline |
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{\footnotesize TOTAL }& |
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{\footnotesize $_{+0.653, -0.613}$ }& |
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{\footnotesize $_{+0.616, -0.607}$ }& |
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{\footnotesize $_{+0.624, -0.596}$ }\\ |
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| \end{tabular}{\footnotesize \par} |
\end{tabular}{\footnotesize \par} |
| %\end{ruledtabular} |
%\end{ruledtabular} |
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Line 271 Channel&
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Line 284 Channel&
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| \clearpage |
\clearpage |
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\section{Conclusion} |
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In this analysis we presented of the $\sigma_{t\bar{t}}$ in the tau + jets channel using 4951.86 pb$^{-1}$ |
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of integrated luminosity. This cross section was $8.46\;\;_{-1.33}^{+1.38}\;\;({\textrm{stat}})$. |
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\clearpage |
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