--- ttbar/p20_taujets_note/Introduction.tex	2011/05/18 21:30:39	1.1
+++ ttbar/p20_taujets_note/Introduction.tex	2011/06/01 01:20:54	1.2
@@ -2,23 +2,22 @@
 \newpage
 \section{\label{sec:intro}\boldmath{Introduction}}
 
-\noindent Since its discovery at the Fermilab TEVATRON collider in 1995, the top quark has been one 
+\noindent Since its discovery at the Fermilab Tevatron collider in 1995, the top quark has been one 
 of the most important topics in High Energy Physics. The study of its production rate and
-properties allows us to perform precision tests of standard model (SM) predictions as well as
-represents a chance of observing possible deviations from such predictions. 
+properties allows us to perform precision tests of the Standard Model (SM) predictions. 
 Amongst all subsequent top decays, the process $t \rightarrow Wb \rightarrow \tau \nu_{\tau} b$
 represents one of the most important tools for probing beyond-SM physics. For instance, 
-the MSSM (Minimal Supersymmetric Standard Model) \cite{Charged Higgs Theory} predicts 
-the existence of the decay $t \rightarrow H^{+}b$ if $m_{H_{-}^{+}} < m_{t} - m_{b}$.
+the MSSM (Minimal Supersymmetric Standard Model) predicts 
+the existence of the decay $t \rightarrow H^{\pm}b$ if $m_{H^{\pm}} < m_{t} - m_{b}$ \cite{Charged Higgs Theory}.
 As the Higgs-fermion coupling is proportional to the latter's 
 mass, the subsequent decay of a charged Higgs boson into a $\tau$ lepton
 is much more favored than its decays into $e$'s and $\mu$'s.
-Therefore, for high values of tan $\beta$ (the ratio of the vacuum expectation values
+Therefore, for high values of $\tan\beta$ (the ratio of the vacuum expectation values
 of the two Higgs doublets) the charged Higgs preferentially decays to $\tau \nu_{\tau}$,
 which increases the branching ratio (BR) of $t \rightarrow \tau \nu_{\tau} b$ relative
 to the SM prediction. Thus, any non-standard flavor- and
-mass-dependent could produce a significant effect on the $\tau$ production channel. In this
-respect, the work presented here represents an important test of the SM predictions as well as
+mass-dependent could produce a significant effect on the $\tau$ production channel. As this
+analyis is limited to SM only in consists of an important test of the SM predictions as well as
 one step further on the investigation of non-SM processes.
 
 
@@ -26,14 +25,17 @@ In this analysis we study the process wh
 $\tau$ lepton and its associated neutrino, while the other $W$ boson decays into 
 a quark-antiquark pair. The $\tau$ is the heaviest lepton and its prompt decay into other
 particles and the probability of being faked by electrons, muons and jets
-makes its reconstruction and identification much more difficult than other top decays.
+makes its reconstruction and identification  more difficult than other leptonic decays of the top.
 
 Here we focus on events where the $\tau$ decays hadronically, 
-meaning to one or three charged hadrons, zero or more neutral hadrons and a tau neutrino.
-This implies that our signal consists of a final state with four or more jets. 
+meaning to one or more charged hadrons, zero or more neutral hadrons and a tau neutrino. Thus
+this analysis is sensitive to 65\% of all $\tau$ decays.
+This particular $\tau$ decay mode plus 2 $b$ jets produce a final state with four or more jets. 
+Therefore we look for signal events with ate least 4 high-$p_{T}$ jets including 2 $b$ jets
+at least one $\tau$ and large $\not\!\! E_{T}$.
 Figures \ref{fig:feynman} and \ref{fig:pie} show respectively the Feynman diagram that decribes
 the process $t\bar{t} \rightarrow \tau + jets$ and the pie chart of top decay.
-In Section \ref{sec:dataset} we discuss or signal and main backgrounds.
+In Section \ref{sec:dataset} we discuss the signal and main backgrounds.
 
 \begin{figure}[h]
 \includegraphics[scale=0.50]{plots/feynman}
@@ -44,7 +46,7 @@ In Section \ref{sec:dataset} we discuss
 \newpage
 
 \begin{figure}[t]
-\includegraphics[scale=0.40]{plots/pie}
+\includegraphics[scale=0.40]{plots/top_pair_branching_frac}
 \caption{Top quark decay pie chart.}
 \label{fig:pie}
 \end{figure}
@@ -52,13 +54,13 @@ In Section \ref{sec:dataset} we discuss
 %\clearpage
 
 The present work is the third measurement of the $t\bar{t}$ cross section in the $\tau + jets$ 
-channel performed with the D\O\ detector. Previous results \cite{p14_note,p17_note} used using p14 RunI
-and p17 RunIIa Data and are summarized in Table \ref{previous} (only statistical uncertainties are shown).
+channel performed with the D0 detector. Previous results using p14
+and p17 data \cite{p14_note,p17_note} summarized in Table 1 (only statistical uncertainties are shown).
 
 \begin{table}[htbp]
 \begin{center}
 \begin{tabular}{|c|r|} \hline
-Data set ($pb^{-1}$)  & cross section ($pb$)        \\ \hline
+$\int \mathcal{L}\mbox{d}t$ ($\mbox{pb}^{-1}$)  & cross section ($\mbox{pb}$)        \\ \hline
 
 \hline
 
@@ -73,13 +75,13 @@ p17 (974.2) & \multicolumn{1}{c|}{$6.90\
 \end{table}
 
  
-The main improvements upon previous p17 analysis are listed below:
+The main improvements over the previous p17 analysis are listed below:
 
 \begin{itemize}
 \item 5 times more data (RunIIb1, RunIIb2 and RunIIb3). 
-\item Trigger used: we use a new set of multijet triggers that represents a gaim of ~ 10\% in the final efficiency.
+\item We use a new set of multijet triggers that represents a gain of ~ 10\% in the final efficiency.
 \item Use of vertex confirmed jets.
 \item Tau energy scale added to the analysis.
-\item Improved neural net (NN) optimization.
-\item New set of p20 b-tag TRF's.
+\item Improved event neural net (NN) optimization.
+\item New set of p20 b-tag tag-rate functions (TRF's).
 \end{itemize}