\section{Strategy} \subsection{\label{sub:Signal-characteristics}Signal characteristics} \subsubsection{Parton level MC} First of all we want to examine the properties of our signal. For these purposes we used MC simulated samples (\textasciitilde{}10K events each) generated with ALPGEN \cite{ALPGEN} interfaced to Pythia \cite{PYTHIA} for showering and fragmentation. \paragraph{$t\bar{t}$} First of all we wanted to look at the properties of the top quark itself. Figure \ref{t-jets} shows the $\eta$, $\phi$ and $P_{T}$ distributions. % \begin{figure} \subfigure[$P_{T}$ of b-quarks]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/pt_tjets}}\subfigure[$\eta$ of b-quarks]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/eta_tjets}} \subfigure[$\phi$ of b-quarks]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/phi_tjets}} \caption{Properties of t-quarks at the parton level in signal MC sample, $P_{T}$> 15 GeV} \begin{centering}\label{t-jets}\par\end{centering} \end{figure} \paragraph{$\tau$ and $\not\!\! E_{T}$} The unique property of $\tau$ (compared to other leptons) is that it emits neutrino in its decay before it even reaches detector volume, contributing to the missing energy of the event. For this reason the $\tau$, available for measurement is not the same as physical $\tau$ produced. Figure \ref{cap:MC taus} demonstrates how a sizable fraction of $\tau$ momentum goes missing. The plots of $\tau$ $\eta$ (Figure \ref{cap:MC taus}) and transverse mass with $\not\!\! E_{T}$ thus are done for the visible part of $\tau$ This is to be compared with the $e+jets$ channel (Figure \ref{cap:MC elecs}). As one can observe, the {}``total'' $\tau$ leptons behave very simmilar to electrons, as of cause expected. However, after taking into account the lost part of the $\tau$ energy situation becomes very different. % \begin{figure} \subfigure[Parton level $\not E_{T}$ for the signal MC (red is total, green- visible)]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/met_mc}} \subfigure[mT of MC $\tau$ and $\not E_{T} $ (red is total, green- visible)]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/mt_tau_met_mc}} \subfigure[$\eta$ of the MC $\tau$ in signal MC (red is total, green- visible)]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/eta_tau_mc}} \subfigure[$P_{T}$ of the MC $\tau$ in signal MC (red is total, green- visible)]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/pt_tau_mc}} \subfigure[Visible energy fraction of $\tau$ in signal MC]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/visable_fraction}} \caption{Properties of $\not\!\! E_{T}$ and $\tau$ at the parton level in signal MC sample} \begin{centering}\label{cap:MC taus}\par\end{centering} \end{figure} % \begin{figure} \subfigure[Parton level $\not E_{T}$ for the signal MC (red is total, green- visible)]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/met_mc_elec}} \subfigure[mT of MC electron and $\not E_{T} $ (red is total, green- visible)]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/mt_tau_met_mc_elec}} \subfigure[$\eta$ of the MC electron in signal MC (red is total, green- visible)]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/eta_tau_mc_elec}} \subfigure[$P_{T}$ of the MC electron in signal MC (red is total, green- visible)]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/pt_tau_mc_elec}} \caption{Properties of $\not\!\! E_{T}$ and electron at the parton level in $t\bar{t}\rightarrow e+jets$ MC sample} \begin{centering}\label{cap:MC elecs}\par\end{centering} \end{figure} \paragraph{Jets} b - jets are shown on Figure \ref{b-jets} while the product of W decay are shown on Figure \ref{not b-jets}. This however doesn't account for all the jets that will be reconstructed. Figure \ref{not b-jets-all} demonstrates all the non-b quarks and gluons in a $t\bar{t}$ event. % \begin{figure} \subfigure[Number of b-quarks]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/nbquarks}} \subfigure[$P_{T}$ of b-quarks]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/pt_bjets}} \subfigure[$\eta$ of b-quarks]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/eta_bjets}} \subfigure[$\phi$ of b-quarks]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/phi_bjets}} \caption{Properties of b-quarks at the parton level in signal MC sample, $P_{T}$> 15 GeV} \begin{centering}\label{b-jets}\par\end{centering} \end{figure} % \begin{figure} \subfigure[Number of light quarks from the W decay]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/nlightquarks}} \subfigure[$P_{T}$ of light quarks from the W decay]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/pt_notbjets}} \subfigure[$\eta$ of light quarks from the W decay]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/eta_notbjets}} \subfigure[$\phi$ of light quarks from the W decay]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/phi_notbjets}} \caption{Properties of light quarks from the W decay at the parton level in signal MC sample, $P_{T}$> 15 GeV} \begin{centering}\label{not b-jets}\par\end{centering} \end{figure} % \begin{figure} \subfigure[Number of not b-quarks]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/nlightquarks_all}} \subfigure[$P_{T}$ of not b-quarks]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/pt_notbjets_all}} \subfigure[$\eta$ of not b-quarks ]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/eta_notbjets_all}} \subfigure[$\phi$ of not b-quarks ]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/phi_notbjets_all}} \caption{Properties of all the light quarks and gluons in an event at the parton level in signal MC sample, $P_{T}$> 15 GeV} \begin{centering}\label{not b-jets-all}\par\end{centering} \end{figure} \subsubsection{Detector signature (reconstructed Monte Carlo)} Now we need to find out how well our experiment observes and reconstructs this physical process. The $t\bar{t}\rightarrow\tau+jets$ Monte Carlo file was processed through the detailed D0 Detector simulation. Jets are reconstructed, using 0.5 radius cone (in $\eta-\phi$). Taus are identified using tau ID algorithm and we apply 0.8 cut on the $\tau$ selection neural net (section \ref{sub:tau--ID}). \paragraph{$\tau$ and $\not\!\! E_{T}$} We can see that for reconstructed $\tau$'s $mT(of$ $\tau$ $and$ $\not E_{T})$ (Figure \ref{cap:reco tau}) doesn't look as good as for MC taus (Figure \ref{cap:MC taus}). We observe a noticeable \char`\"{}tail\char`\"{} above 80 GeV. % \begin{figure} \subfigure[Reconstructed $\not E_{T}$ for the signal MC ]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/met_reco}} \subfigure[mT of MC $\tau$ and $\not E_{T} $ reconstructed ]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/mt_tau_met_reco}} \subfigure[$\eta$ of the MC tau in signal MC reconstructed ]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/eta_tau_reco}} \subfigure[ $P_{T}$ of the $\tau$ ]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/pt_tau_reco}} \caption{Properties of detector reconstructed $\not\!\! E_{T}$ and $\tau$ in signal MC sample} \begin{centering}\label{cap:reco tau}\par\end{centering} \end{figure} \paragraph{Jets} Before b-tagging (section \ref{sub:B-tagging}) one can't separate b-jets from non-b jets, so we don't make a distinction at this point. Most important variables are the number of jets and $\eta$ and $P_{T}$ distributions (Figure \ref{jets1}). % \begin{figure} \subfigure[Number of jets]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/njets}} \subfigure[$P_{T}$ of jets]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/jetpt}} \subfigure[$\eta$ of jets]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/eta_jets}} \subfigure[$\phi$ of jets]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/phi_jets}} \caption{Properties of the jets in signal MC sample, $P_{T}$> 15 GeV} \begin{centering}\label{jets1}\par\end{centering} \end{figure} Jets are arranged in the order of their $P_{T}$: leading (highest), sub-leading etc. We can see on Figure \ref{jets1} that we typically have 4 or 5 jets in an event. It is interesting to compare the leading jet to the fourth and fifth jets (Figure \ref{jets2}). We can see that jets after the third are very soft, as expected. % \begin{figure} \subfigure[1st jet]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/jet0pt}} \subfigure[2nd jet]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/jet1pt}} \subfigure[3rd jet]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/jet2pt}} \subfigure[4th jet]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/jet3pt}} \subfigure[5th jet]{\includegraphics[scale=0.3]{MS_thesis/proposal_plots/jet4pt}} \caption{$P_{T}$ distributions for jets in signal MC sample (including $\tau$)} \begin{centering}\label{jets2}\par\end{centering} \end{figure} \subsection{Backgrounds} Two main distinctive features of the signal limit the spectrum of important backgrounds. In order to be relevant the process must have high (>3) number of jets as well as sizable (>15 GeV) $\not\!\! E_{T}$. All the candidate processes are listed in Table \ref{backgrounds}. The cross section listed include the branching fractions into $\tau$ We can conclude that two dominant background sources are QCD ({}``fake $\tau$'') and W+4jets. These two sources were taken into account in these analysis. % \begin{table} \begin{tabular}{|l|l|c|} \hline \multicolumn{1}{||l|}{Background}& \multicolumn{1}{||l|}{Description}& \multicolumn{1}{||l||}{Cross Section}\tabularnewline \hline $W+jjjj\rightarrow\tau\nu jjjj$& Has identical signature to the signal& $\sim$18 pb \tabularnewline \hline $Z/\gamma+jjj\rightarrow\tau\tau jjj$ & $\tau$ is usually found as a jet& $\sim$2.6 pb\tabularnewline \hline $WZ\rightarrow\tau\nu jj$& needs two extra jet (can be gluon emission) & $\sim$0.2 pb\tabularnewline \hline $WW\rightarrow\tau\nu jj$& needs two extra jet (can be gluon emission) & $\sim$0.5 pb\tabularnewline \hline single top & small cross section, but has b-jets & $\sim$0.5 pb\tabularnewline \hline QCD & Any 4-jet event, that doesn't have a real $\tau$ in it& $>$100 nb \tabularnewline \hline \end{tabular}\centering \caption{Background sources, relevant for the $\tau+jets$ analysis. Branching into hadronic $\tau$ had been applied \cite{l+jets}} \label{backgrounds} \end{table} \section{Dataset} As will be demonstrated in section \ref{sub:Running-trigsim} the optimal (that is most efficient) combination of triggers for this analysis is: \begin{itemize} \item The Higgs Missing $H_{T}$ trigger (MHT30\_3CJT5) \item The ALLJET trigger (4JT10) \end{itemize} Together they yield over 85\% signal acceptance and they'd been running unprescaled for most of D0 stable operation. The data skim, utilizing both of these triggers would be optimal for this analysis. Until the technical issues involved in its production are fully resolved, we are using the ALLJET skim \cite{Luminosity}, which only contains the data, collected by the 4JT10 (and its subsequent versions). Such skim is only 70\% efficient for the signal, but it's the closest available for our needs at the moment. The full PASS2 ALLJET skim had been processed through the standard D0 top group data quality criteria, discarding bad luminosity blocks, at the same time computing the recorded lumi. The results are represented in table \ref{lumi1}. Therefore the total luminosity available for the analysis amounts to $349\pm23$ $pb^{-1}$ \cite{alljet} % \begin{table} \begin{tabular}{|c|c|c|c|} \hline Stage& Luminosity ($pb^{-1})$& Relative Size (\%)& Absolute Size (\%)\tabularnewline \hline \hline Delivered& 482.6& 100& 100\tabularnewline \hline Recorded& 411.6& 85.3& 85.3\tabularnewline \hline Good& 352.5& 85.6& 73.0\tabularnewline \hline Reconstructed& 349.3& 99.1& 72.4\tabularnewline \hline \end{tabular} \caption{The results of luminosity calculation for the PASS2 ALLJET top skim} \label{lumi1} \end{table} The table \ref{lumi2} demonstrates the breakdown of this luminosity between the different trigger versions. % \begin{table} \begin{tabular}{|c|c|c|} \hline Trigger version& Trigger name& Luminosity ($pb^{-1})$\tabularnewline \hline \hline 8.0& 4JT10& 19.4\tabularnewline \hline 9.0& 4JT10& 21.2\tabularnewline \hline 10.0& 4JT10& 15.1\tabularnewline \hline 11.0& 4JT10& 57.3\tabularnewline \hline 12.0& 4JT12& 196\tabularnewline \hline 13.0& JT2\_4JT12L\_HT& 13.5\tabularnewline \hline 13.1& JT2\_4JT12L\_HT& 27.8\tabularnewline \hline 13.3& JT2\_4JT12L\_HT& 0\tabularnewline \hline \end{tabular} \caption{Luminosity of the ALLJET skim for different D0 trigger list versions} \label{lumi2} \end{table}