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1.1     ! uid12904    1: \section{Analysis outline}
        !             2: Up to this point we have presented the data sample used in this analysis (Section \ref{sub:datasample})
        !             3: the Monte Carlo samples and corrections applied to them (Sections \ref{sub:mcsample} and \ref{sub:mcsample_xseccorr}),
        !             4: the trigger used and its simulation (Section \ref{sec:trig_param}) and the object ID
        !             5: method (Section \ref{sec:objects}). Now we describe the next steps of the analysis
        !             6: towards the final crosse section measurement:
        !             7: 
        !             8: \begin{itemize}
        !             9: \item Preselection (section \ref{sub:Preselection}): at least 4 jets, at least one $\tau$ with NN$>$0.3 and $p_{T}>10$ GeV/$c$,
        !            10: 15 GeV $\leq$ $\not\!\! E_{T}$ $\leq$ 500 GeV and $\not\!\! E_{T}$ significance $>$4.0. 
        !            11: \item $\tau$- and b-ID cuts (section \ref{sub:Results-of-the}): at least one good $\tau$ lepton 
        !            12: candidate and at least one tight NN b-tag are required.  
        !            13: \item Topological NN (section \ref{sub:NN-variables}): a
        !            14: feed-forward NN's is trained in order to provide signal-background separation. The NN
        !            15: was optimized by testing different sets of topological variables as its inputs and by applying
        !            16: different $\not\!\! E_{T}$ significance cuts.
        !            17: \item Topological Variables (section \ref{sub:Topo}): section showing final analysis plots of topological
        !            18: variables of interest.
        !            19: \item Cross Section (section \ref{sub:xsect}) The signal fraction determination is 
        !            20: combined with integrated luminosity measurement to calculate the cross section.  
        !            21: Systematic uncertainties are determined by fluctuating the significant components 
        !            22: up and down by one standard deviation one at a time, propagating it through the entire procedure. 
        !            23: \end{itemize}
        !            24: 
        !            25: \section{\label{sub:Preselection}Preselection}
        !            26: 
        !            27: The preselection is the first step of the analysis. The cuts presented here were chosen in order to provide the best
        !            28: background reduction and enhance the $t\bar{t}$  content at this point. The cuts are the similar to those used in the 
        !            29: p17 analysis \cite{p17_note} except that for this time we opted to optimize the value of $\not\!\! E_{T}$ 
        !            30: significance along with the sets of variables we used as inputs to NN training (Section \ref{sub:NN}). 
        !            31: 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}.
        !            32: 
        !            33: %\begin{itemize}
        !            34: %\item One $\tau$ lepton. 
        !            35: %\item $\not\!\! E_{T}$ arising from both the W vertex and $\tau$
        !            36: %decay. 
        !            37: %\item At least 4 jets including two $b$-jets. 
        !            38: %\end{itemize}
        !            39: 
        !            40: \begin{itemize}
        !            41: \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
        !            42: \item at least one $\tau$ with NN$>$0.3 and $p_{T}>10$ GeV 
        !            43: \item 15 GeV $\leq$ $\not\!\! E_{T}$ $\leq$ 500 GeV
        !            44: \item $\not\!\! E_{T}$ significance $\geq$ 4.0 
        !            45: \item No isolated electron or muon. This is done in order to ensure orthogonality with other \dzero \hspace{1pt} 
        !            46: measurements (\cite{l+jets} and \cite{dilepton}) - events that pass the lepton preselection cuts from these measurements 
        !            47: were vetoed. Also events that pass the all-jets analysis preselection cuts (described in the alljet analysis note \cite{alljet}) 
        !            48: are rejected here.
        !            49: \end{itemize}
        !            50: 
        !            51:  
        !            52: 
        !            53: %\begin{figure}
        !            54: %\label{cap:metl}
        !            55: %\includegraphics[scale=0.6]{plots/metl}% Here is how to import EPS art
        !            56: %\caption{$\not\!\! E_{T}$ significance for QCD-dominated data (black), $W+jets$ (blue) and $t\bar{t}\rightarrow\tau+jets$ (red).}
        !            57: %\label{cap:met_significance} 
        !            58: %\end{figure}
        !            59: 
        !            60: Among all preselection cuts one of them requires a more detailed description at this point since it represents
        !            61: an improvement upon the old p17 analysis: $\not\!\! E_{T}$ significance.
        !            62: Missing transverse energy significance is a measure of the likelihood of $\not\!\! E_{T}$
        !            63: arising from physical sources. It is computed from calculated resolutions of physical objects (jets, electrons,
        !            64: muons and unclustered energy) \cite{p17_note,METsig}. Initially no $\not\!\! E_{T}$ significance
        !            65: was applied neither on MC nor on data. In this analysis we decided
        !            66: to optimize the $\not\!\! E_{T}$ significance cut along with the NN optimization itself. 
        !            67: After finishing the $\not\!\! E_{T}$ significance optimization 
        !            68: part we went back and applied the optimized cut along with the non-optimized NNelec cut only to MC. 
        !            69: The entire optimization procedure is described in Section \ref{sub:NN-optimization}.
        !            70: 
        !            71: 
        !            72: In data, initially the sample contained approximately 650 million events and the number of preselected events
        !            73: (once again, without $\not\!\! E_{T}$ significance applied) is approximately 2.8 million events.
        !            74: 
        !            75: 
        !            76: Another relevant aspect of the preselection is the usage of Particle Selector (only applied to MC samples). 
        !            77: In this step we aimed to select a particular $\ttbar$ final state, namely, we split $W$ decay 
        !            78: into $W \rightarrow e/\mu /\tau $ and 
        !            79: tracked separate efficiencies for each of these processes. In this step we selected hadronic decays of tau,
        !            80: and at the same events where tau decays into electrons and muons were put into $e + jets$ and $\mu + jets$ samples.
        !            81: As in p17, we decided to do not split the dilepton sample in different lepton flavors.
        !            82: 
        !            83: Before proceeding to the next step, it is important to describe the result of the preselection
        !            84: in terms of its efficiencies since all the rest of analysis strongly depends on the cuts applied at this level. 
        !            85: As previously described, $t\bar{t}$ were generated by ALPGEN. In ALPGEN, different process with different
        !            86: numbers of partons have different cross-sections and number of events. This fact must be taken into account when calculating the 
        !            87: efficiencies, namely, efficiencies must be properly scaled to the luminosity (4951.85 pb$^{-1}$) of the sample. Tables 
        !            88: \ref{ttbar_alp} and III show the number beforementioned for $t\bar{t} \rightarrow$ lepton + jets
        !            89: %VI and VII show the number beforementioned for $t\bar{t} \rightarrow$ lepton + jets
        !            90: and $t\bar{t} \rightarrow$ dilepton respectively.
        !            91: 
        !            92: \begin{table}[h]
        !            93: \begin{center}
        !            94: \begin{tabular}{|c|r|r|r|} \hline
        !            95: Process   & \# of events & cross-section (pb) & alpgen weight    \\ \hline
        !            96: 
        !            97: \hline
        !            98: 
        !            99: 
        !           100: 0 light parton     &  \multicolumn{1}{c|}{777068}   &  \multicolumn{1}{c|}{1.4} &  \multicolumn{1}{c|}{0.00892}  \\ \hline
        !           101: 
        !           102: 
        !           103: 1 light parton      &  \multicolumn{1}{c|}{457782} &  \multicolumn{1}{c|}{0.577} &  \multicolumn{1}{c|}{0.00624} \\ \hline
        !           104: 
        !           105: 
        !           106: $\geq$ 2 light partons     &  \multicolumn{1}{c|}{321166}   &  \multicolumn{1}{c|}{0.267} &  \multicolumn{1}{c|}{0.00412} \\ \hline
        !           107: \end{tabular}
        !           108: \caption{$t\bar{t} \rightarrow$ lepton + jets ALPGEN weights.}
        !           109: \end{center}
        !           110: \label{ttbar_alp} 
        !           111: \end{table}
        !           112: 
        !           113: 
        !           114: \begin{table}[h]
        !           115: \begin{center}
        !           116: \begin{tabular}{|c|r|r|r|} \hline
        !           117: Process   & \# of events & cross-section (pb) & alpgen weight    \\ \hline
        !           118: 
        !           119: \hline
        !           120: 
        !           121: 
        !           122: 0 light parton     &  \multicolumn{1}{c|}{749642}   &  \multicolumn{1}{c|}{0.352} &  \multicolumn{1}{c|}{0.00233}  \\ \hline
        !           123: 
        !           124: 
        !           125: 1 light parton      &  \multicolumn{1}{c|}{452177} &  \multicolumn{1}{c|}{0.142} &  \multicolumn{1}{c|}{0.00156} \\ \hline
        !           126: 
        !           127: 
        !           128: $\geq$ 2 light partons     &  \multicolumn{1}{c|}{281453}   &  \multicolumn{1}{c|}{0.068} &  \multicolumn{1}{c|}{0.00119} \\ \hline
        !           129: \end{tabular}
        !           130: \caption{$t\bar{t} \rightarrow$ dilepton ALPGEN weights.}
        !           131: \end{center}
        !           132: \label{dilep_alp} 
        !           133: \end{table}
        !           134: 
        !           135: Tables \ref{taujets_cutflow}, \ref{ejets_cutflow}, \ref{mujets_cutflow} and
        !           136: \ref{dilep_cutflow} show cut flows for all preselection cuts applied to different $\ttbar$ decays 
        !           137: (only statistical uncertainties are shown).
        !           138: 
        !           139: %
        !           140: 
        !           141: \begin{table}[h]
        !           142: %\begin{center}
        !           143: \begin{tabular}{ccccc}
        !           144: \hline
        !           145: Selection & Events & Relative  & Cumulative \\ \hline Initial & 11164 & &  \\ 
        !           146: Particle selector & 2412 &  $ 21.60 \pm 0.03 ~\% $ &  $ 21.60 \pm 0.03~\% $ \\
        !           147: Duplicate events removal & 2411 &  $ 99.98 \pm 0.01 ~\% $ &  $ 21.60 \pm 0.03~\% $ \\
        !           148: Event quality & 2315 &  $ 96.00 \pm 0.04 ~\% $ &  $ 20.74 \pm 0.03~\% $   \\
        !           149: Jet selection & 1307 &  $ 59.45 \pm 0.09 ~\% $ &  $ 11.70 \pm 0.03~\% $  \\ 
        !           150: Vertex selection & 1296 &  $ 99.18 \pm 0.02 ~\% $ &  $ 11.61 \pm 0.03~\% $  \\ 
        !           151: Electron veto & 1282 &  $ 98.93 \pm 0.01 ~\% $ &  $ 11.49 \pm 0.03~\% $ \\ 
        !           152: Muon veto & 1282 &  $ 99.93 \pm 0.01 ~\% $ &  $ 11.48 \pm 0.03~\% $ \\ 
        !           153: MET selection & 1218 &  $ 95.05 \pm 0.05 ~\% $ &  $ 10.91 \pm 0.02~\% $  \\ 
        !           154: MET significance & 772 &  $ 63.39 \pm 0.12 ~\% $ &  $ 6.92 \pm 0.02~\% $  \\
        !           155: NN tau cut & 394 &  $ 53.51 \pm 0.15 ~\% $ &  $ 3.70 \pm 0.02~\% $  \\ \hline
        !           156: 
        !           157: \end{tabular}
        !           158: \caption{Preselection $t\overline{t}\rightarrow\tau+jets$ cut flow} 
        !           159: %\end{center}
        !           160: \label{taujets_cutflow}
        !           161: \end{table}
        !           162: 
        !           163: %\newpage
        !           164: 
        !           165: \begin{table}[t]
        !           166: %\begin{center}
        !           167: \begin{tabular}{ccccc}
        !           168: \hline
        !           169: Selection & Events & Relative  & Cumulative \\ \hline Initial & 11164 & &  \\ 
        !           170: Particle selector & 4385 &  $ 39.28 \pm 0.04 ~\% $ &  $ 39.28 \pm 0.04~\% $ \\
        !           171: Duplicate event removal & 4383 &  $ 99.96 \pm 0.01 ~\% $ &  $ 39.26 \pm 0.04~\% $ \\
        !           172: Event quality & 4207 &  $ 95.97 \pm 0.03 ~\% $ &  $ 37.68 \pm 0.04~\% $   \\
        !           173: Jet selection & 1923 &  $ 45.71 \pm 0.07 ~\% $ &  $ 17.22 \pm 0.03~\% $  \\ 
        !           174: Vertex selection & 1907 &  $ 99.20 \pm 0.02 ~\% $ &  $ 17.08 \pm 0.03~\% $  \\ 
        !           175: Electron veto & 1048 &  $ 54.94 \pm 0.10 ~\% $ &  $ 9.39 \pm 0.02~\% $ \\ 
        !           176: Muon veto & 1047 &  $ 99.95 \pm 0.01 ~\% $ &  $ 9.38 \pm 0.02~\% $ \\ 
        !           177: MET selection & 1002 &  $ 95.64 \pm 0.05~\% $ &  $ 8.97 \pm 0.02~\% $  \\ 
        !           178: MET significance & 669 &  $ 66.74 \pm 0.13 ~\% $ &  $ 5.99 \pm 0.02~\% $  \\
        !           179: NN tau cut & 395 &  $ 59.12 \pm 0.16 ~\% $ &  $ 3.54 \pm 0.02~\% $  \\ \hline
        !           180: 
        !           181: \end{tabular}
        !           182: \caption{Preselection $t\overline{t}\rightarrow e+jets$ cut flow}
        !           183: %\end{center}
        !           184: \label{ejets_cutflow}
        !           185: \end{table}
        !           186: 
        !           187: %\clearpage
        !           188: 
        !           189: \begin{table}[t]
        !           190: %\begin{center}
        !           191: \begin{tabular}{ccccc}
        !           192: \hline
        !           193: Selection & Events & Relative  & Cumulative \\ \hline Initial & 11164 & &  \\ 
        !           194: Particle selector & 4367 &  $ 39.12 \pm 0.04 ~\% $ &  $ 39.12 \pm 0.04~\% $ \\
        !           195: Duplicate event removal & 4366 &  $ 99.96 \pm 0.04 ~\% $ &  $ 39.10 \pm 0.04~\% $ \\
        !           196: Event quality & 4189 &  $  95.95 \pm 0.03 ~\% $ &  $ 37.52 \pm 0.04~\% $   \\
        !           197: Jet selection & 1990 &  $ 47.52 \pm 0.07 ~\% $ &  $ 17.83 \pm 0.03~\% $  \\ 
        !           198: Vertex selection & 1975 &  $ 99.23 \pm 0.02 ~\% $ &  $ 17.69 \pm 0.03~\% $  \\ 
        !           199: Electron veto & 1967 &  $ 99.59 \pm 0.01 ~\% $ &  $ 17.62 \pm 0.03~\% $ \\ 
        !           200: Muon veto &  1170 &  $ 59.48 \pm 0.09 ~\% $ &  $ 10.48 \pm 0.02~\% $ \\ 
        !           201: MET selection & 1127 &  $ 96.31 \pm 0.04~\% $ &  $ 10.09 \pm 0.02~\% $  \\ 
        !           202: MET significance & 812 &  $ 72.06 \pm 0.11 ~\% $ &  $ 7.27 \pm 0.02~\% $  \\
        !           203: NN tau cut & 186 &  $ 22.95 \pm 0.13 ~\% $ &  $ 1.67 \pm 0.01~\% $  \\ \hline
        !           204: 
        !           205: \end{tabular}
        !           206: \caption{Preselection $t\overline{t}\rightarrow \mu +jets$ cut flow}
        !           207: %\end{center}
        !           208: \label{mujets_cutflow}
        !           209: \end{table}
        !           210: 
        !           211: 
        !           212: \begin{table}[b]
        !           213: %\begin{center}
        !           214: \begin{tabular}{ccccc}
        !           215: \hline
        !           216: Selection & Events & Relative  & Cumulative \\ \hline Initial & 2799 & &  \\ 
        !           217: Particle selector & 2799 &  $ 100.00 \pm 0.00 ~\% $ &  $ 100.00 \pm 0.00~\% $ \\
        !           218: Duplicate event removal & 2799 &  $ 100.00 \pm 0.00 ~\% $ &  $ 100.00 \pm 0.00~\% $ \\
        !           219: Event quality & 2685 &  $ 95.92 \pm 0.02 ~\% $ &  $ 95.92 \pm 0.02~\% $   \\
        !           220: Jet selection & 145 &  $ 5.41 \pm 0.02 ~\% $ &  $ 5.19 \pm 0.02~\% $  \\ 
        !           221: Vertex selection & 144 &  $ 99.32 \pm 0.03 ~\% $ &  $ 5.16 \pm 0.02~\% $  \\ 
        !           222: Electron veto & 110 &  $ 76.14 \pm 0.13 ~\% $ &  $ 3.93 \pm 0.01~\% $ \\ 
        !           223: Muon veto & 83 &  $ 75.08 \pm 0.16 ~\% $ &  $ 2.95 \pm 0.01~\% $ \\ 
        !           224: MET selection & 80 &  $ 96.45 \pm 0.08~\% $ &  $ 2.84 \pm 0.01~\% $  \\ 
        !           225: MET significance & 60 &  $ 75.32 \pm 0.19 ~\% $ &  $ 2.14 \pm 0.01~\% $  \\
        !           226: NN tau cut & 38 &  $ 63.21 \pm 0.24 ~\% $ &  $ 1.35 \pm 0.01~\% $  \\ \hline
        !           227: 
        !           228: \end{tabular}
        !           229: \caption{Preselection $t\overline{t}\rightarrow l+l$ cut flow}
        !           230: %\end{center}
        !           231: \label{dilep_cutflow}
        !           232: \end{table}
        !           233: 
        !           234: \clearpage
        !           235: 
        !           236: 
        !           237: 
        !           238: %\clearpage