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\section{Systematic uncertainties}

The following components are added in quadrature to estimate the total systematic uncertainty.

\subsection{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.


\subsection{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}.


\subsection{Jet Energy Resolution and Jet ID}

\noindent The jet energy resolution (JER) systematic is determined by shifiting the jet energy 
resolution by $\pm 1 \sigma$ in all MC samples.

\subsection{Trigger}
\noindent For this systematics, the level of agreement (as a function of $H_T$) when applying the trigger
turn-on curves to 4-jet data events was measured. We then used the ratio between the predicted and the 
actual trigger decision as a function of $H_T$ to assign a error due to the trigger modeling. All MC events
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. 


\subsection{b-quark fragmentation}
\noindent This uncertainty is estimated using the standard procedure described in \cite{bfrag} by reweighting $t\bar{t}$ events
using different fragmentation functions.

\subsection{\boldmath $b$-tagging}

\noindent b-tagging uncertainty effects are taken into account by varying the
systematic and statistical uncertainties on the MC tagging weights.

These uncertainties (which are computed using standard D0 b ID group tools) arise form several independent sources \cite{bID-p20}:

\begin{itemize}
\item B-jet tagging parameterization. 
\item C-jet tagging parameterization. 
\item Light jet tagging parameterization (negative tag rate).
%\item Systematic uncertainties on the scale factors $SF_{hf}$ and $SF_{ll}$
%are derived from the statistical error due to finite MC statistics. 
\item Semi-leptonic b-tagging efficiency parameterization in MC and in data
(System 8). 
\item Taggability. This includes the statistical uncertainty due to finite statistic
in the samples from which it had been derived and systematic, reflecting
the (neglected) taggability dependence on the jet multiplicity. 
\end{itemize}


\subsection{\boldmath $\tau$ identification}

\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
these systematics are 9.5\%, 3.5\% and 5.0\% for taus type 1, 2 and 3 respectively. However in this analysis we chose 
to treat taus types 1 and 2 together. This led us to combine their uncertainties in the following way

\begin{center}
\begin{equation}
sys_{12} = \displaystyle \sqrt{\epsilon_{1}^{2} \cdot f_{1}^{2} + \epsilon_{2}^{2} \cdot f_{2}^{2}}
\end{equation}
\end{center}

\noindent where $\epsilon_{1}$ and $\epsilon_{2}$ are the $\tau$ ID efficiencies for taus types 1 and 2 respectively and 
$f_{1}$ and $f_{2}$ are the fractions of taus types 1 (0.16) and 2 (0.84) respectively.


\subsection{\label{sub:qcd_syst}QCD modeling}
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 
use the same sample to evaluate the associated uncertainties. We did this
by reweighting topological event NN for QCD template 
(``loose-tight'' $\tau$), so that it matches the one for ``tight'' $\tau$ data exactly 
(electroweak backgrounds were subtracted). 
%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. 

\subsection{$W$ and $Z$ scale 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 $Zbb$ and $Zcc$ events, both with an uncertainty of 20\%.


\subsection{Template statistics}
When we performed the template fit to data (Section \ref{sub:NN}) the QCD template had limited statistics 
(1132 events for taus types 1 and 2 and 4487 events for taus type 3). We have to take the 
statistical uncertainty in this histogram as one of the cross section systematics. It was calculated by 
varying the content of each bin of the QCD template NN distribution within its uncertainty and observing 
how the cross section result changed.

\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
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
and finally measuring the up and down values of the cross section.

\subsection{PDF}
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}
package tool on {\sc PYTHIA} $t\bar{t}$ MC. We then assigned the relative PDF uncertainty obtained with {\sc PYTHIA}
on the {\sc ALPGEN} $t\bar{t}$ MC.

\subsection{Luminosity}
Here we take the D0 standard measured uncertainty on luminosity of 6.1$\%$ .


Tables \ref{cap:Syst1} and \ref{cap:Syst2} summarize all of these uncertainty sources and shows how the resulting cross section shifts.

%\clearpage
%

%\section{Summary \label{sec:summary}}


%

%\section{Summary \label{sec:summary}}

\begin{table}[h]
\caption{Systematic uncertainties on $\sigma(t\bar{t})$ (in pb) for NNelec $>$ 0.9.}
%\begin{ruledtabular}
{\footnotesize }\begin{tabular}{cccc}
\hline 
Channel&
{\footnotesize $\tau$+jets types 1 and 2 }&
{\footnotesize $\tau$+jets type 3 }&
{\footnotesize Combined }\\
{\footnotesize Tau Energy Scale }&
{\footnotesize $_{+0.068, -0.102}$ }&
{\footnotesize $_{+0.340, -0.306}$ }&
{\footnotesize $_{+0.136, -0.136}$ }\\
{\footnotesize Jet Energy Scale }&
{\footnotesize $_{+0.051, -0.034}$ }&
{\footnotesize $_{+0.051, -0.085}$ }&
{\footnotesize $_{+0.051, -0.000}$ }\\
{\footnotesize Jet Energy Resolution }&
{\footnotesize $_{+0.102, -0.051}$ }&
{\footnotesize $_{+0.204, -0.034}$ }&
{\footnotesize $_{+0.119, -0.052}$ }\\
{\footnotesize Jet ID }&
{\footnotesize $_{+0.204, -0.204}$ }&
{\footnotesize $_{+0.153, -0.153}$ }&
{\footnotesize $_{+0.204, -0.204}$ }\\
{\footnotesize b-tag }&
{\footnotesize $_{+0.562, -0.493}$ }&
{\footnotesize $_{+0.493, -0.426}$ }&
{\footnotesize $_{+0.544, -0.477}$ }\\
{\footnotesize b-fragmentation }&
{\footnotesize $_{+0.102, -0.102}$ }&
{\footnotesize $_{+0.068, -0.068}$ }&
{\footnotesize $_{+0.085, -0.085}$ }\\
{\footnotesize QCD Modeling }&
{\footnotesize $_{+0.340, -0.340}$ }&
{\footnotesize $_{+0.221, -0.221}$ }&
{\footnotesize $_{+0.324, -0.305}$ }\\
{\footnotesize $\tau$ ID }&
{\footnotesize $_{+0.272, -0.272}$ }&
{\footnotesize $_{+0.306, -0.306}$ }&
{\footnotesize $_{+0.290, -0.290}$ }\\
{\footnotesize Trigger }&
{\footnotesize $_{+0.256, -0.256}$ }&
{\footnotesize $_{+0.238, -0.238}$ }&
{\footnotesize $_{+0.256, -0.256}$ }\\
%{\footnotesize $\tau$ triggering }&
%{\footnotesize $_{+xxxx, -xxxx}$ }&
%{\footnotesize $_{+xxxx, -xxxx}$ }&
%{\footnotesize $_{+xxxx, -xxxx}$ }\\
{\footnotesize W Scale Factor }&
{\footnotesize $_{+0.034, -0.034}$ }&
{\footnotesize $_{+0.034, -0.034}$ }&
{\footnotesize $_{+0.034, -0.034}$ }\\
{\footnotesize Z Scale Factor }&
{\footnotesize $_{+0.072, -0.072}$ }&
{\footnotesize $_{+0.072, -0.072}$ }&
{\footnotesize $_{+0.048, -0.048}$ }\\
{\footnotesize Template statistics }&
{\footnotesize $_{+0.156, -0.156}$ }&
{\footnotesize $_{+0.204, -0.204}$ }&
{\footnotesize $_{+0.168, -0.168}$ }\\
{\footnotesize Signal contamination}&
{\footnotesize $_{+0.153, -0.153}$ }&
{\footnotesize $_{+0.255, -0.272}$ }&
{\footnotesize $_{+0.188, -0.170}$ }\\
{\footnotesize PDF }&
{\footnotesize $_{+0.097, -0.084}$ }&
{\footnotesize $_{+0.188, -0.198}$ }&
{\footnotesize $_{+0.092, -0.081}$ }\\
\hline
{\footnotesize TOTAL }&
{\footnotesize $_{+0.839, -0.791}$ }&
{\footnotesize $_{+0.882, -0.820}$ }&
{\footnotesize $_{+0.843, -0.779}$ }\\

\end{tabular}{\footnotesize \par}
%\end{ruledtabular}
\label{cap:Syst1} 
\end{table}


\begin{table}[h]
\caption{Systematic uncertainties on $\sigma(t\bar{t})$ (in pb) when no NNelec cut is applied.}
%\begin{ruledtabular}
{\footnotesize }\begin{tabular}{cccc}
\hline 
Channel&
{\footnotesize $\tau$+jets types 1 and 2 }&
{\footnotesize $\tau$+jets type 3 }&
{\footnotesize Combined }\\
{\footnotesize Tau Energy Scale }&
{\footnotesize $_{+0.101, -0.002}$ }&
{\footnotesize $_{+0.238, -0.255}$ }&
{\footnotesize $_{+0.102, -0.017}$ }\\
{\footnotesize Jet Energy Scale }&
{\footnotesize $_{+0.016, -0.001}$ }&
{\footnotesize $_{+0.017, -0.000}$ }&
{\footnotesize $_{+0.016, -0.000}$ }\\
{\footnotesize Jet Energy Resolution }&
{\footnotesize $_{+0.084, -0.086}$ }&
{\footnotesize $_{+0.017, -0.034}$ }&
{\footnotesize $_{+0.068, -0.085}$ }\\
{\footnotesize Jet ID }&
{\footnotesize $_{+0.169, -0.169}$ }&
{\footnotesize $_{+0.017, -0.017}$ }&
{\footnotesize $_{+0.153, -0.153}$ }\\
{\footnotesize b-tag }&
{\footnotesize $_{+0.424, -0.375}$ }&
{\footnotesize $_{+0.358, -0.306}$ }&
{\footnotesize $_{+0.425, -0.375}$ }\\
{\footnotesize b-fragmentation }&
{\footnotesize $_{+0.069, -0.069}$ }&
{\footnotesize $_{+0.102, -0.102}$ }&
{\footnotesize $_{+0.068, -0.068}$ }\\
{\footnotesize QCD Modeling }&
{\footnotesize $_{+0.271, -0.273}$ }&
{\footnotesize $_{+0.153, -0.136}$ }&
{\footnotesize $_{+0.225, -0.256}$ }\\
{\footnotesize $\tau$ ID }&
{\footnotesize $_{+0.220, -0.220}$ }&
{\footnotesize $_{+0.204, -0.204}$ }&
{\footnotesize $_{+0.221, -0.221}$ }\\
{\footnotesize Trigger }&
{\footnotesize $_{+0.204, -0.204}$ }&
{\footnotesize $_{+0.170, -0.170}$ }&
{\footnotesize $_{+0.204, -0.204}$ }\\
%{\footnotesize $\tau$ triggering }&
%{\footnotesize $_{+xxxx, -xxxx}$ }&
%{\footnotesize $_{+xxxx, -xxxx}$ }&
%{\footnotesize $_{+xxxx, -xxxx}$ }\\
{\footnotesize W Scale Factor }&
{\footnotesize $_{+0.034, -0.034}$ }&
{\footnotesize $_{+0.034, -0.034}$ }&
{\footnotesize $_{+0.034, -0.034}$ }\\
{\footnotesize Z Scale Factor }&
{\footnotesize $_{+0.072, -0.072}$ }&
{\footnotesize $_{+0.072, -0.072}$ }&
{\footnotesize $_{+0.048, -0.048}$ }\\
{\footnotesize Template statistics }&
{\footnotesize $_{+0.118, -0.118}$ }&
{\footnotesize $_{+0.170, -0.170}$ }&
{\footnotesize $_{+0.102, -0.102}$ }\\
{\footnotesize Signal contamination}&
{\footnotesize $_{+0.050, -0.052}$ }&
{\footnotesize $_{+0.136, -0.187}$ }&
{\footnotesize $_{+0.051, -0.051}$ }\\
{\footnotesize PDF }&
{\footnotesize $_{+0.097, -0.084}$ }&
{\footnotesize $_{+0.188, -0.198}$ }&
{\footnotesize $_{+0.092, -0.081}$ }\\
\hline
{\footnotesize TOTAL }&
{\footnotesize $_{+0.653, -0.613}$ }&
{\footnotesize $_{+0.616, -0.607}$ }&
{\footnotesize $_{+0.624, -0.596}$ }\\

\end{tabular}{\footnotesize \par}
%\end{ruledtabular}
\label{cap:Syst2} 
\end{table}



\clearpage
\section{Conclusion}

In this analysis we presented of the $\sigma_{t\bar{t}}$ in the tau + jets channel using 4951.86 pb$^{-1}$
of integrated luminosity. This cross section was $8.46\;\;_{-1.33}^{+1.38}\;\;({\textrm{stat}})$.

\clearpage