--- ttbar/p20_taujets_note/Systematics.tex	2011/05/18 21:30:39	1.1
+++ ttbar/p20_taujets_note/Systematics.tex	2011/06/01 01:20:54	1.2
@@ -1,15 +1,15 @@
 \newpage
 \section{Systematic uncertainties}
 
-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.
 
-\subsection{JES}
+\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{TES}
+\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}.
@@ -21,7 +21,10 @@ by its uncertainty as given in \cite{tes
 resolution by $\pm 1 \sigma$ in all MC samples.
 
 \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
+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. 
 
 
@@ -32,9 +35,9 @@ using different fragmentation functions.
 \subsection{\boldmath $b$-tagging}
 
 \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.
 
-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}:
 
 \begin{itemize}
 \item B-jet tagging parameterization. 
@@ -44,22 +47,22 @@ These errors (which are computed using s
 %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 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
 the (neglected) taggability dependence on the jet multiplicity. 
 \end{itemize}
 
 
-\subsection{\boldmath $\tau$ ID systematics}
+\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 
-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
 
 \begin{center}
 \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{center}
 
@@ -67,19 +70,19 @@ sys_{12} = \displaystyle \sqrt{\epsilon_
 $f_{1}$ and $f_{2}$ are the fractions of taus types 1 (0.16) and 2 (0.84) respectively.
 
 
-\subsection{\label{sub:qcd_syst}QCD systematics}
-As explained in the section \ref{sub:Variables} we use the control (b-veto) data set to 
+\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. The way it was 
-done is by reweighting topological event NN for QCD template 
+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 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 
 %models the QCD-dominated data very well. 
 
-\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
-of 1.52 and 1.67 are applied to Z + bb and Z + cc events, both with an uncertainty of 20\%.
+\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}
@@ -90,7 +93,7 @@ varying the content of each bin of the Q
 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
+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.
@@ -98,11 +101,11 @@ and finally measuring the up and down va
 \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 Pythia $t\bar{t}$ MC. We then assigned the relative PDF uncertainty obtained with Pythia on the Alpgen
-$t\bar{t}$ MC.
+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 D\O\ standard measured uncertainty on luminosity of 6.1$\%$ .
+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.
@@ -186,6 +189,11 @@ Channel&
 {\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}
@@ -262,6 +270,11 @@ Channel&
 {\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}
@@ -271,3 +284,10 @@ Channel&
 
 
 \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
+