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\section{Analysis outline} Up to this point we have presented the data sample used in this analysis (Section \ref{sub:datasample}) the Monte Carlo samples and corrections applied to them (Sections \ref{sub:mcsample} and \ref{sub:mcsample_xseccorr}), the trigger used and its simulation (Section \ref{sec:trig_param}) and the object ID method (Section \ref{sec:objects}). Now we describe the next steps of the analysis towards the final crosse section measurement: \begin{itemize} \item Preselection (section \ref{sub:Preselection}): at least 4 jets, at least one $\tau$ with NN$>$0.3 and $p_{T}>10$ GeV/$c$, 15 GeV $\leq$ $\not\!\! E_{T}$ $\leq$ 500 GeV and $\not\!\! E_{T}$ significance $>$4.0. \item $\tau$- and b-ID cuts (section \ref{sub:Results-of-the}): at least one good $\tau$ lepton candidate and at least one tight NN b-tag are required. \item Topological NN (section \ref{sub:NN-variables}): a feed-forward NN's is trained in order to provide signal-background separation. The NN was optimized by testing different sets of topological variables as its inputs and by applying different $\not\!\! E_{T}$ significance cuts. \item Topological Variables (section \ref{sub:Topo}): section showing final analysis plots of topological variables of interest. \item Cross Section (section \ref{sub:xsect}) The signal fraction determination is combined with integrated luminosity measurement to calculate the cross section. Systematic uncertainties are determined by fluctuating the significant components up and down by one standard deviation one at a time, propagating it through the entire procedure. \end{itemize} \section{\label{sub:Preselection}Preselection} The preselection is the first step of the analysis. The cuts presented here were chosen in order to provide the best background reduction and enhance the $t\bar{t}$ content at this point. The cuts are the similar to those used in the p17 analysis \cite{p17_note} except that for this time we opted to optimize the value of $\not\!\! E_{T}$ significance along with the sets of variables we used as inputs to NN training (Section \ref{sub:NN}). Cuts shown below were applied to samples shown in Table \ref{used_mc} as well as to data as shown in Section \ref{sub:datasample}. %\begin{itemize} %\item One $\tau$ lepton. %\item $\not\!\! E_{T}$ arising from both the W vertex and $\tau$ %decay. %\item At least 4 jets including two $b$-jets. %\end{itemize} \begin{itemize} \item At least 4 jets with $p_{T}>15$ GeV and $\eta <$2.5, with leading (in $p_{T}$) jet $p_{T}>35$ GeV and second and third jets have $p_{T}>25$ GeV \item at least one $\tau$ with NN$>$0.3 and $p_{T}>10$ GeV \item 15 GeV $\leq$ $\not\!\! E_{T}$ $\leq$ 500 GeV \item $\not\!\! E_{T}$ significance $\geq$ 4.0 \item No isolated electron or muon. This is done in order to ensure orthogonality with other \dzero \hspace{1pt} measurements (\cite{l+jets} and \cite{dilepton}) - events that pass the lepton preselection cuts from these measurements were vetoed. Also events that pass the all-jets analysis preselection cuts (described in the alljet analysis note \cite{alljet}) are rejected here. \end{itemize} %\begin{figure} %\label{cap:metl} %\includegraphics[scale=0.6]{plots/metl}% Here is how to import EPS art %\caption{$\not\!\! E_{T}$ significance for QCD-dominated data (black), $W+jets$ (blue) and $t\bar{t}\rightarrow\tau+jets$ (red).} %\label{cap:met_significance} %\end{figure} Among all preselection cuts one of them requires a more detailed description at this point since it represents an improvement upon the old p17 analysis: $\not\!\! E_{T}$ significance. Missing transverse energy significance is a measure of the likelihood of $\not\!\! E_{T}$ arising from physical sources. It is computed from calculated resolutions of physical objects (jets, electrons, muons and unclustered energy) \cite{p17_note,METsig}. Initially no $\not\!\! E_{T}$ significance was applied neither on MC nor on data. In this analysis we decided to optimize the $\not\!\! E_{T}$ significance cut along with the NN optimization itself. After finishing the $\not\!\! E_{T}$ significance optimization part we went back and applied the optimized cut along with the non-optimized NNelec cut only to MC. The entire optimization procedure is described in Section \ref{sub:NN-optimization}. In data, initially the sample contained approximately 650 million events and the number of preselected events (once again, without $\not\!\! E_{T}$ significance applied) is approximately 2.8 million events. Another relevant aspect of the preselection is the usage of Particle Selector (only applied to MC samples). In this step we aimed to select a particular $\ttbar$ final state, namely, we split $W$ decay into $W \rightarrow e/\mu /\tau $ and tracked separate efficiencies for each of these processes. In this step we selected hadronic decays of tau, and at the same events where tau decays into electrons and muons were put into $e + jets$ and $\mu + jets$ samples. As in p17, we decided to do not split the dilepton sample in different lepton flavors. Before proceeding to the next step, it is important to describe the result of the preselection in terms of its efficiencies since all the rest of analysis strongly depends on the cuts applied at this level. As previously described, $t\bar{t}$ were generated by ALPGEN. In ALPGEN, different process with different numbers of partons have different cross-sections and number of events. This fact must be taken into account when calculating the efficiencies, namely, efficiencies must be properly scaled to the luminosity (4951.85 pb$^{-1}$) of the sample. Tables \ref{ttbar_alp} and III show the number beforementioned for $t\bar{t} \rightarrow$ lepton + jets %VI and VII show the number beforementioned for $t\bar{t} \rightarrow$ lepton + jets and $t\bar{t} \rightarrow$ dilepton respectively. \begin{table}[h] \begin{center} \begin{tabular}{|c|r|r|r|} \hline Process & \# of events & cross-section (pb) & alpgen weight \\ \hline \hline 0 light parton & \multicolumn{1}{c|}{777068} & \multicolumn{1}{c|}{1.4} & \multicolumn{1}{c|}{0.00892} \\ \hline 1 light parton & \multicolumn{1}{c|}{457782} & \multicolumn{1}{c|}{0.577} & \multicolumn{1}{c|}{0.00624} \\ \hline $\geq$ 2 light partons & \multicolumn{1}{c|}{321166} & \multicolumn{1}{c|}{0.267} & \multicolumn{1}{c|}{0.00412} \\ \hline \end{tabular} \caption{$t\bar{t} \rightarrow$ lepton + jets ALPGEN weights.} \end{center} \label{ttbar_alp} \end{table} \begin{table}[h] \begin{center} \begin{tabular}{|c|r|r|r|} \hline Process & \# of events & cross-section (pb) & alpgen weight \\ \hline \hline 0 light parton & \multicolumn{1}{c|}{749642} & \multicolumn{1}{c|}{0.352} & \multicolumn{1}{c|}{0.00233} \\ \hline 1 light parton & \multicolumn{1}{c|}{452177} & \multicolumn{1}{c|}{0.142} & \multicolumn{1}{c|}{0.00156} \\ \hline $\geq$ 2 light partons & \multicolumn{1}{c|}{281453} & \multicolumn{1}{c|}{0.068} & \multicolumn{1}{c|}{0.00119} \\ \hline \end{tabular} \caption{$t\bar{t} \rightarrow$ dilepton ALPGEN weights.} \end{center} \label{dilep_alp} \end{table} Tables \ref{taujets_cutflow}, \ref{ejets_cutflow}, \ref{mujets_cutflow} and \ref{dilep_cutflow} show cut flows for all preselection cuts applied to different $\ttbar$ decays (only statistical uncertainties are shown). % \begin{table}[h] %\begin{center} \begin{tabular}{ccccc} \hline Selection & Events & Relative & Cumulative \\ \hline Initial & 11164 & & \\ Particle selector & 2412 & $ 21.60 \pm 0.03 ~\% $ & $ 21.60 \pm 0.03~\% $ \\ Duplicate events removal & 2411 & $ 99.98 \pm 0.01 ~\% $ & $ 21.60 \pm 0.03~\% $ \\ Event quality & 2315 & $ 96.00 \pm 0.04 ~\% $ & $ 20.74 \pm 0.03~\% $ \\ Jet selection & 1307 & $ 59.45 \pm 0.09 ~\% $ & $ 11.70 \pm 0.03~\% $ \\ Vertex selection & 1296 & $ 99.18 \pm 0.02 ~\% $ & $ 11.61 \pm 0.03~\% $ \\ Electron veto & 1282 & $ 98.93 \pm 0.01 ~\% $ & $ 11.49 \pm 0.03~\% $ \\ Muon veto & 1282 & $ 99.93 \pm 0.01 ~\% $ & $ 11.48 \pm 0.03~\% $ \\ MET selection & 1218 & $ 95.05 \pm 0.05 ~\% $ & $ 10.91 \pm 0.02~\% $ \\ MET significance & 772 & $ 63.39 \pm 0.12 ~\% $ & $ 6.92 \pm 0.02~\% $ \\ NN tau cut & 394 & $ 53.51 \pm 0.15 ~\% $ & $ 3.70 \pm 0.02~\% $ \\ \hline \end{tabular} \caption{Preselection $t\overline{t}\rightarrow\tau+jets$ cut flow} %\end{center} \label{taujets_cutflow} \end{table} %\newpage \begin{table}[t] %\begin{center} \begin{tabular}{ccccc} \hline Selection & Events & Relative & Cumulative \\ \hline Initial & 11164 & & \\ Particle selector & 4385 & $ 39.28 \pm 0.04 ~\% $ & $ 39.28 \pm 0.04~\% $ \\ Duplicate event removal & 4383 & $ 99.96 \pm 0.01 ~\% $ & $ 39.26 \pm 0.04~\% $ \\ Event quality & 4207 & $ 95.97 \pm 0.03 ~\% $ & $ 37.68 \pm 0.04~\% $ \\ Jet selection & 1923 & $ 45.71 \pm 0.07 ~\% $ & $ 17.22 \pm 0.03~\% $ \\ Vertex selection & 1907 & $ 99.20 \pm 0.02 ~\% $ & $ 17.08 \pm 0.03~\% $ \\ Electron veto & 1048 & $ 54.94 \pm 0.10 ~\% $ & $ 9.39 \pm 0.02~\% $ \\ Muon veto & 1047 & $ 99.95 \pm 0.01 ~\% $ & $ 9.38 \pm 0.02~\% $ \\ MET selection & 1002 & $ 95.64 \pm 0.05~\% $ & $ 8.97 \pm 0.02~\% $ \\ MET significance & 669 & $ 66.74 \pm 0.13 ~\% $ & $ 5.99 \pm 0.02~\% $ \\ NN tau cut & 395 & $ 59.12 \pm 0.16 ~\% $ & $ 3.54 \pm 0.02~\% $ \\ \hline \end{tabular} \caption{Preselection $t\overline{t}\rightarrow e+jets$ cut flow} %\end{center} \label{ejets_cutflow} \end{table} %\clearpage \begin{table}[t] %\begin{center} \begin{tabular}{ccccc} \hline Selection & Events & Relative & Cumulative \\ \hline Initial & 11164 & & \\ Particle selector & 4367 & $ 39.12 \pm 0.04 ~\% $ & $ 39.12 \pm 0.04~\% $ \\ Duplicate event removal & 4366 & $ 99.96 \pm 0.04 ~\% $ & $ 39.10 \pm 0.04~\% $ \\ Event quality & 4189 & $ 95.95 \pm 0.03 ~\% $ & $ 37.52 \pm 0.04~\% $ \\ Jet selection & 1990 & $ 47.52 \pm 0.07 ~\% $ & $ 17.83 \pm 0.03~\% $ \\ Vertex selection & 1975 & $ 99.23 \pm 0.02 ~\% $ & $ 17.69 \pm 0.03~\% $ \\ Electron veto & 1967 & $ 99.59 \pm 0.01 ~\% $ & $ 17.62 \pm 0.03~\% $ \\ Muon veto & 1170 & $ 59.48 \pm 0.09 ~\% $ & $ 10.48 \pm 0.02~\% $ \\ MET selection & 1127 & $ 96.31 \pm 0.04~\% $ & $ 10.09 \pm 0.02~\% $ \\ MET significance & 812 & $ 72.06 \pm 0.11 ~\% $ & $ 7.27 \pm 0.02~\% $ \\ NN tau cut & 186 & $ 22.95 \pm 0.13 ~\% $ & $ 1.67 \pm 0.01~\% $ \\ \hline \end{tabular} \caption{Preselection $t\overline{t}\rightarrow \mu +jets$ cut flow} %\end{center} \label{mujets_cutflow} \end{table} \begin{table}[b] %\begin{center} \begin{tabular}{ccccc} \hline Selection & Events & Relative & Cumulative \\ \hline Initial & 2799 & & \\ Particle selector & 2799 & $ 100.00 \pm 0.00 ~\% $ & $ 100.00 \pm 0.00~\% $ \\ Duplicate event removal & 2799 & $ 100.00 \pm 0.00 ~\% $ & $ 100.00 \pm 0.00~\% $ \\ Event quality & 2685 & $ 95.92 \pm 0.02 ~\% $ & $ 95.92 \pm 0.02~\% $ \\ Jet selection & 145 & $ 5.41 \pm 0.02 ~\% $ & $ 5.19 \pm 0.02~\% $ \\ Vertex selection & 144 & $ 99.32 \pm 0.03 ~\% $ & $ 5.16 \pm 0.02~\% $ \\ Electron veto & 110 & $ 76.14 \pm 0.13 ~\% $ & $ 3.93 \pm 0.01~\% $ \\ Muon veto & 83 & $ 75.08 \pm 0.16 ~\% $ & $ 2.95 \pm 0.01~\% $ \\ MET selection & 80 & $ 96.45 \pm 0.08~\% $ & $ 2.84 \pm 0.01~\% $ \\ MET significance & 60 & $ 75.32 \pm 0.19 ~\% $ & $ 2.14 \pm 0.01~\% $ \\ NN tau cut & 38 & $ 63.21 \pm 0.24 ~\% $ & $ 1.35 \pm 0.01~\% $ \\ \hline \end{tabular} \caption{Preselection $t\overline{t}\rightarrow l+l$ cut flow} %\end{center} \label{dilep_cutflow} \end{table} \clearpage %\clearpage