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\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}