%
%  Top talk at Carleton
%
\documentstyle[epsfig,colordvi,pagecount]{slides}

\input latex.macros
\input top.macros
\def\DZero{D$\mbox{0\kern-.55em /}$}
\def\mDZero{{\rm D}\mbox{0\kern-.55em /}}
\def\mGeVcc{{\rm GeV\, c^2}}
%

\newcommand{\tit}[1] {
        \begin{center}
        \normalsize
        \fbox{\Red{#1}} \vspace{.25in}
        \small
        \end{center}
}


\def\met{\mathbin{E\mkern - 11mu/_T}}

\begin{document}

\small

\tit{Top Quark Properties}

\Start
\vspace{0.5in}
\begin{center}
Pekka Sinervo\\
{\it University of Toronto}
\end{center}

\vspace{0.5in}

\Red{Overview}

\tiny
\begin{itemize}
\item What We Learn From the Top Quark
\item Overview of Experiments
\item Top quark mass and cross section
\item Single top production
\item Top quark $P_T$\ distribution
\item On to Run II
\end{itemize}

\begin{flushright}
Work done in collaboration with Pierre Savard \\
and Andrew Robinson
\end{flushright}

\pagebreak
%
%  Intro to SM 
%
\tit{The Top Quark in the Standard Model}

\small
The SM ``needs'' a massive top quark
\tiny
\begin{itemize}
	\item $b$\ quark requires an SU(2) partner
	\begin{itemize}
		\item suppression of FCNC decays
		\item $e^+e^-\rightarrow b\bar{b}$\ scattering
	\end{itemize}
	\item Many loop effects in SM driven by $M_{top}$
	\begin{itemize}
		\item $W/Z$\ boson mass ratio
		\item $b-\bar{b}$\ mixing
		\item Rare K decays
	\end{itemize}
\end{itemize}
\vspace{1.8in}
\vbox{
\vskip+0.0in
\hskip+0.0in
\special{psfile=figures/physics_figures/b_bbar_mixing.eps  hscale= 80.0 vscale= 80.0}
\vskip-0.0in
}

\small
Direct observation of top in 1995
\tiny
\begin{itemize}
	\item Confirmed all these predictions
	\item Gave us a ``free quark'' system to study
	\item[\Blue{$\Rightarrow$}] \Blue{New frontier in particle physics}
\end{itemize}

\pagebreak

%
%  Some history
%
\tit{Recent History of Top}

CDF and \DZero\ collected $\sim100$~\invpb\ of data in 92-96
\tiny
\begin{itemize}
	\item 1.8 TeV $p\bar{p}$\ collisions
	\item Collected events with
	\begin{itemize}
		\item High $P_T$\ leptons ($P_T\gessim10$~\GeVc)
		\item $\MEt>25$~GeV
		\item High $P_T$\ jets ($P_T\gessim100$~\GeVc)
	\end{itemize}
	\item In 1995, presented evidence for $t\bar{t}$\ production \\[0.1in]
\end{itemize}

\small
Subsequent studies have strengthened this
\tiny
\begin{itemize}
	\item Different techniques used to look at the same data
	\begin{itemize}
		\item Kinematic distributions
		\item Neural network approaches
	\end{itemize}
	\item Have verified consistency in all channels
	\begin{itemize}
		\item See reasonable signals in $\tau$\ lepton final
states
		\item All hadronic modes are also understood
	\end{itemize}
\end{itemize}

\pagebreak

%
\tit{SM Top Quark Phenomenology} 

\small
Top quarks decay via the weak force
\tiny
\begin{itemize}
	\item Predict $\sim100$\% $t\rightarrow W^+ b$
	\item Lifetime depends on mass
	\item For heavy top ($M_{top}\gessim 100-120$ \GeVcc), decays
	before it hadronises \\[0.1in]
\end{itemize}

\small
Can be viewed as a ``pure'' charged current
\tiny
\begin{eqnarray}
\Gamma_{\rm top} &=& {{G_F M_t^3}\over{8\sqrt{2} \pi}} 
   \left( 1 - {{M_W^2}\over{M_t^2}} \right)^2 
   \left( 1 + 2{{M_W^2}\over{M_t^2}} \right) \nonumber \\
&\sim& 175\ {\rm MeV}\ \left( {{M_t}\over{M_W}} \right)^3\ \sim\ 2\
{\rm GeV} \nonumber
\end{eqnarray}
\begin{itemize}
	\item Toponium doesn't have time to form
	\item $T$~mesons $\sim$\ degenerate (if there was time...)
\\[0.1in]
\end{itemize}

\small
Decay dominated by ``longitudinal $W^+$''
\tiny
\begin{itemize}
	\item Means the $W^+$\ prefers helicity 0
	\item Result of large top and $W^+$\ mass
\end{itemize}	

\pagebreak

\tit{What Do Top Decays Tell Us?}

\small
SM predicts ``pure'' $V-A$\ decay
\tiny
\begin{itemize}
	\item clear test of polarisation at decay vertex
\begin{eqnarray}
	{{W_{\rm long}}\over{W_{\rm T}}} \sim {{1}\over{2}} 
\left( {{M_t}\over{M_W}} \right)^2 \sim 2.2 \nonumber
\end{eqnarray}
	\item $V_{ts}$\ CKM matrix elements
	\item Constraints on other SM parameters (eg. $A_{LR}$)
	\item Effectively another consistency check of SM \\[0.1in]
\end{itemize}

\small
Sensitive to some classes of ``new physics''
\tiny
\begin{itemize}
	\item Higgs couples strongly to top
	\item Could decay into a SUSY $H^+$
\begin{eqnarray}
 &t& \rightarrow H^+ b \nonumber \\
  && \quad \mrightdownarrow \tau^+ \nu_\tau \nonumber
\end{eqnarray}

	\item Top quark might be ``special'' in unexpected way
	\begin{itemize}
		\item New physics that couples to \ttbar\ system
		\item Low Scale Gravity a good recent example
	\end{itemize}
\end{itemize}

\pagebreak
%
%  What do we have now
%
\tit{The Status of Top Today}

\small
CDF has now detected top in virtually all decay modes
\tiny
\begin{itemize}
	\item Lepton + Jets mode (for mass analysis)
	\begin{itemize}
		\item lepton $P_T>20$~\GeVc\ and $\mMEt>20$~GeV
		\item $\ge3$\ jets, $E_T>15$~GeV and $|\eta|<2$
		\item Require 1 $b$-tagged jet OR a 4th jet
		with $E_T>15$
		\item[\Blue{$\Rightarrow$}] \Blue{76 candidates}\
		(expect $31\pm7$\ bkg) \\[0.05in]
	\end{itemize}
%
	\item Dileptons
	\begin{itemize}
		\item 2 leptons with $P_T>20$~\GeVc
		\item Remove Drell-Yan and $Z^\circ$\ background
		\item[\Blue{$\Rightarrow$}] \Blue{9 candidates} 
		($2.4\pm0.5$\ events bkg) \\[0.05in]
	\end{itemize}

	\item All hadronic decays
	\begin{itemize}
		\item between 5 and 8 jets ($E_T > 15$~GeV and
		$|\eta|<2.0$)
		\item $\sum E_T > 300$\ GeV + additional kinematic
cuts
		\item[\Blue{$\Rightarrow$}] \Blue{Observe 187 $b$-tagged jets}
		($142\pm11$\ expected bkg)
	\end{itemize}

\end{itemize}

\small
Used these samples for top quark measurements
\pagebreak
%
%  What are the Interesting properties
%
\tit{What are the Interesting Top Properties?}

\tiny
\begin{itemize}
	\item Top Quark Mass
	\begin{itemize}
		\item SM constrains it to $M_W/M_Z$ 
		\item Important consistency check of theory
			\\[0.05in]
	\end{itemize}
	\item Top Quark Production Cross Section
	\begin{itemize}
		\item Predicted by QCD with less uncertainties than 
		$\sigma_b$
		\item Look for single top production 
			\\[0.05in]
	\end{itemize}
	\item Top Quark Decay Rates
	\begin{itemize}
		\item Measured $t\rightarrow W^+ b/
			t\rightarrow W^+ q$
		\item Searched for FCNC such as $t\rightarrow Z^\circ c$
			\\[0.05in]
	\end{itemize}
	\item Top Quark Decay Kinematics
	\begin{itemize}
		\item SM expects decay to be polarized
		\item Have made first measurement of polarization
	\end{itemize}
\end{itemize}

\pagebreak

%
%  Top Mass result
%
\tit{Top Quark Mass}

\small
Measurements now limited by systematic uncertainties
\tiny
\begin{itemize}
	\item Overall systematic uncertainty is $\sim 5$~\GeVcc
	\begin{itemize}
		\item Dominated by uncertainties in soft gluon 
		contributions and energy scale
	\end{itemize}
	\item Statistical uncertainty limit our ability to constrain
this
\end{itemize}

\begin{center}
\epsfysize=3.5in
\epsffile[30 140 520 630]{ljm_likfit1.ps}
\end{center}

\small
The final Run I values are 
\tiny
\begin{eqnarray}
	M_{top} &=& 176.0 \pm 6.5 \ \mGeVcc\ {\rm (CDF)} \nonumber \\
	M_{top} &=& 172.1 \pm 7.1 \ \mGeVcc\ {\rm (\mDZero)} \nonumber \\
	M_{top} &=& 174.3 \pm 5.1 \ \mGeVcc\ {\rm (Run I)} \nonumber
\end{eqnarray}

\pagebreak

\begin{center}
\epsfysize=5.5in
\epsffile[30 140 520 630]{mw_vs_mtop_lep_slc.ps}
\end{center}

\pagebreak

%
%  Top Cross Section
%
\tit{Top Quark Production Cross Section}

\small
The cross section obtained by a fit to 
\tiny
\begin{itemize}
	\item Lepton + jets rate
	\item Dileptons rate
	\item All hadronic event rate
\end{itemize}

\small
Depends on $M_{top}$\ because of acceptance
\begin{eqnarray}
\sigma_{\mttbar} &=& 7.6^{+1.8}_{-1.5}\ {\rm pb} \nonumber
\end{eqnarray}

\begin{center}
\epsfysize=3.5in
\epsffile[30 140 520 630]{xs_theories.ps}
\end{center}

\small
Rarest process ever measured in hadron collider!
\tiny
\begin{itemize}
	\item Theory predictions range from 4.7 to 5.5 pb
\end{itemize}

\pagebreak
\tit{Comparison with \DZero}

Measurements by \DZero\ also quite consistent

\begin{center}
\epsfysize=5.5in
\epsffile[30 140 520 630]{run_i_xsec_table.ps}
\end{center}

\pagebreak

%
%  Single Top Production
%
\tit{Single Top Production}

\small
Single top production is a much lower rate process
\tiny
\begin{itemize}
	\item Sensitive to $\Gamma_{t}$\
	\item Also could have contributions from non-SM sources
			\\[0.05in]
\end{itemize}

\small
There are two primary SM production processes
\tiny
\begin{enumerate}
	\item $t$-channel $W-g$\ fusion $\Rightarrow W^+ b q$\ final state
	\item $s$-channel $W^\ast$\ process 
		$\Rightarrow W^+ b \bar{b}$\ final state
			\\[0.01in]
\end{enumerate}

\begin{center}
\epsfysize=3.0in
\epsffile[30 140 520 630]{single_top_production_diagrams.ps}
\end{center}

\begin{itemize}
	\item Predicted cross sections are $1.7\pm0.3$\ and
$0.7\pm0.1$~pb
\end{itemize}
\pagebreak
%
%  Search for two processes
%
\tit{Search Technique}

\small
Kinematics of processes somewhat different
\tiny
\begin{itemize}
	\item Use almost the same selection for both processes
	\begin{itemize}
		\item Exactly 2 jets with $E_T>15$~Gev and $|\eta|<2.0$
		\item At least one $b$-tagged jet
		\item Require $145\le M_{top}\le 205$~\GeVcc
	\end{itemize}
	\item Differences are
	\begin{itemize}
		\item For $W$-gluon fusion, require exactly one $b$-tag
		\item Have different acceptance
	\end{itemize}
\end{itemize}
\tiny
\begin{center}
\begin{tabular}{lcc}
			&  $W^\ast$	&	$W$-gluon \\[0.05in]
\hline \\
$\sigma_{theory}$\ (pb)		&   $0.73\pm0.10$	&  $1.7\pm0.3$ \\
Integrated luminosity (\invpb)	&  $106\pm4$		&  $106\pm4$   \\
$W+2$~jet acceptance (\%)	&  $ 3.4\pm0.7$		&  $3.3\pm0.6$ \\
SVX $b$-tag efficiency (\%)	&  $37.5\pm3.1$		& $24.8\pm2.0$ \\[0.05in]
\hline \\
Number of expected events	&  $1.0\pm0.2$		&  $1.5\pm0.3$ \\
\end{tabular}
\end{center}

\vspace{.2in}
		
\pagebreak

\tit{Top Mass Reconstruction}

\vspace{.5in}

\begin{center}
\epsfysize=5.5in
\epsffile[30 140 520 630]{single_top_top_mass.ps}
\end{center}

\pagebreak
%
%  Results of search
%
\tit{Results of Search}

\small
Observed 42 events in this sample
\tiny
\begin{itemize}
	\item Largest single background are mis-tags
	\begin{itemize}
		\item $t\bar{t}$\ itself is a \Red{problem}\ now
	\end{itemize}
\end{itemize}

\begin{center}
\begin{tabular}{lc}
Process			&	Event Yield \\[0.05in]
\hline \\
$W b \bar{b} + W c \bar{c}$	&	$ 9.0\pm2.5$	\\
Mistags				&	$ 6.3\pm2.6$	\\
$W c$				&	$ 4.3\pm1.5$	\\
Non-$W$\			&	$ 2.3\pm1.0$	\\
Miscellaneous			&	$ 2.1\pm0.6$	\\
\hline \\
$t\bar{t}$			&	$ 5.7\pm1.3$	\\
$W$-gluon			&	$ 1.5\pm0.3$	\\
$W^\ast$			&	$ 1.0\pm0.3$	\\
\hline \\
Total expected			&	$32 \pm 5$	\\
Observed			&	   42    	\\
\end{tabular}
\end{center}

\small
Not yet sensitive to SM single top rate
\tiny
\begin{itemize}
	\item Can set limits separately on different processes
\end{itemize}
\pagebreak

%
%  Single top from W gluon fusion
%
\tit{Single Top Production from $W$-gluon Fusion}

\small
Can exploit a rapidity correlation
\tiny
\begin{itemize}
	\item Top quark and light quark are in same hemisphere 
	\item We fit the $Q\times\eta_{jet}$\ distributions where
	$Q=Q_{jet}\times Q_{lepton}$
			\\[0.3in]
\end{itemize}

\begin{center}
\epsfysize=3.5in
\epsffile[30 140 520 630]{single_top_q_times_eta.ps}
\end{center}

\small
Perform maximum likelihood fit to signal + backgrounds
\tiny
\begin{itemize}
	\item Constrains single top rate from this process
	\item Fit gives $N_{W-{\rm gluon}}=1.4^{+4.2}_{-3.4}$\ events
\end{itemize}

\begin{eqnarray}
\Rightarrow \sigma_{W-{\rm gluon}} &<& 15.4\ {\rm pb} \nonumber
\end{eqnarray}

\pagebreak

%
%  Single top from W* production
%
\tit{Single Top Production from $W^\ast$\ Production}

\small
Essentially all the information is in the observed yield
\tiny
\begin{itemize}
	\item Some discrimination in top mass distribution
	\item Set upper limit in similar manner
	to $W$-gluon fusion case
		\\[0.1in]
\end{itemize}

\small
Perform maximum likelihood fit to signal + backgrounds
\tiny
\begin{itemize}
	\item Use likelihood function to constrain single top rate
	\item Fit gives $N_{W^\ast}=7.3^{+7.4}_{-6.7}$
\end{itemize}

\begin{eqnarray}
\sigma_{W^\ast} &<& 15.8\ {\rm pb} \nonumber
\end{eqnarray}

\small
So still well away from SM rate
\tiny
\begin{itemize}
	\item Can conclude that there is no huge anomaly
	\item It is a feasable measurement for Run II
\end{itemize}

\pagebreak
%
%  Top Quark Pt Distribution
%
\tit{Top Quark Transverse Momentum Distribution}

\tiny
\begin{itemize}
	\item Goal is to produce \Red{model-independent constraints} on
	the top quark $P_T$ distribution
	\begin{itemize}
		\item Produce a set of confidence limits on 
${{d\sigma_t}\over{dP_T}}$
		\item Limited to large bins ($\Delta P_T = 75$~\GeVc)
	\end{itemize}
	\item Properly correct for resolution smearing and acceptance
	\item Can test models (such as ADD) in which the $P_T$
	spectrum is more sensitive to new physics then the total cross
	section 
\end{itemize}

\begin{center}
\epsfig{file=hill.eps}
\end{center}          

\pagebreak

%
%  Event selection for Top Pt Measurement
%
\tit{Event Selection}

\vspace{0.25in}

\small
Use the ``standard'' lepton + jets event selection:
\tiny
\begin{itemize}
	\item Single isolated $e(\mu)$ having $P_T>20$~\GeVc\ and $|\eta|<1.0$
	\item $\met > 20$~GeV
	\item $\ge 4$~jets, 3 with $E_T>15$~GeV and $|\eta|<2.0$
	\begin{itemize}
		\item fourth with $E_T>8$~GeV, $|\eta|<2.4$
			\\[0.1in]
	\end{itemize}
\end{itemize}

\small
To increase the signal significance, require that 
\tiny
\begin{center}
$N_{\mathrm{jet15}} \ge 4$ \Red{or} $N_{tag} \ge 1$ .
\end{center} 

\small
Kinematically fit event, constraining $M_{top} = 175$~\GeVcc
\tiny
\begin{itemize}
	\item Require $\chi^2 < 10$
	\item[$\Rightarrow$] Left with 61 events 
\end{itemize}

\pagebreak

\tit{Measurement of $P_T$}

Measurements on lepton-side and jet-side are \Red{strongly
correlated!}

\begin{center}
\epsfig{file=correlations.eps}
\end{center}

\tiny
\begin{itemize}
\item Make measurement using only \Red{jet-side} top quarks
\end{itemize}

\pagebreak

\tit{Output of the Fitter}

\begin{center}
\epsfig{file=why.eps}
\end{center}

\Red{Only $\sim 50$\% of top quarks in mass sample with true
$P_T$ in the range $150\le P_T \le 225$~GeV, have reconstructed $P_T$
in the correct bin!}

\pagebreak

\tit{$P_T$ Response Functions}

\small
\Red{Have measured $P_T$\ smearing using MC and detector simulation}

\vspace{0.2in}
\begin{center}
\epsfig{file=res4.eps}
\end{center}

\tiny
\begin{itemize}
	\item Use standard HERWIG MC calculations
	\item Most smearing arises from incorrect jet assignments
\end{itemize}
\pagebreak

\tit{Uncorrected $P_T$\  Distribution}

\begin{center}
\epsfig{file=smear.eps}
\end{center}

\tiny
\begin{itemize}
	\item 61 events pass selection criteria
	\item Background distribution normalized to estimated rate
	\begin{itemize}
		\item We estimate $N_{bgd}=24.6\pm 5.8$\ events
	\end{itemize}
\end{itemize}

\pagebreak

\tit{Resulting Fitted $P_T$\ Distribution}

\small
Perform unbinned likelihood fit to response functions and bkg shapes
\tiny
\begin{itemize}
	\item Fit tagged and untagged events with different templates
	\item Use ``bootstrap'' technique to minimize assumptions 
	about shape of $P_T$ spectrum \Red{within each true bin}
	\item Define
\begin{eqnarray}
		R_i \equiv {{\rm fraction\ in\ {\it i}th\ bin}\over{
			\sigma_{\mttbar}}} \nonumber
\end{eqnarray}
\end{itemize}
\small
Apply $P_T$-dependent acceptance correction
\tiny
\begin{itemize}
	\item Acceptance increases with $P_T$
\end{itemize}

\small
\Red{Acceptance Corrected Results:}
\tiny
\begin{eqnarray}
R_1 & = & 0.29^{+0.18}_{-0.18}\nonumber \\
R_2 & = & 0.42^{+0.18}_{-0.18}\nonumber \\
R_3 & = & 0.29^{+0.12}_{-0.10}\nonumber  \\
R_4 & = & 0.000^{+0.035}_{-0.000} \nonumber
\end{eqnarray}

\pagebreak

\tit{Combining $R_1$ and $R_2$}

\small
$R_1$\ and $R_2$\ have strong negative correlation
\tiny
\begin{itemize}
	\item large uncertainties from fit
	\item Makes sense to combine these into single measurement
\end{itemize}

\begin{center}
\epsfig{file=plot_combined.eps}
\end{center}


\small
Resulting combined fraction of low $P_T$\ top quarks is
\tiny
\begin{eqnarray}
R_1+R_2 = 0.68\pm 0.13 \nonumber
\end{eqnarray}

\pagebreak

\tit{Verification of Methodology}


\small
\Red{Use MC technique to verify robustness of technique}

\vspace{0.10in}

\tiny
\begin{center}
\begin{tabular}{ccc}
Sample & $N_{ev}$ & $N_{bgd}\pm \sigma_{bgd}$ \\[0.05in]
\hline \\
No Tag & 32 & $18.9\pm 5.6$ \\
Tagged & 29 & $6.4 \pm 1.3$ \\
\end{tabular}
\end{center}

\vspace{0.25in}

\small
Perform MC Carlo experiments on random samples of 32 untagged
and 29 tagged events: 
\tiny
\begin{itemize}
\item Assume background in each tagging subsample 
distributed as $N(N_{bgd},\sigma_{bgd})$
\item Draw the appropriate numbers of background and signal events
and run analysis 
\item Compare means of distributions to the expected
SM $P_T$ distribution
\end{itemize}

\pagebreak

%\tit{Monte Carlo Experiments}
\Red{So\dots Does all this work?}
\begin{center}
\epsfig{file=r1pull.eps}
\end{center}
\begin{center}
\epsfig{file=r2pull.eps}
\end{center}
\pagebreak
%\tit{What about $R_3$?}
\begin{center}
\epsfig{file=r3pull.eps}
\end{center}
\begin{center}
\epsfig{file=r3pull_r3big.eps}
\end{center}
Problems in small fraction(4\%) of the pseudo-experiments, flagged
by a very small value of $R_3$.
\pagebreak

\tit{Upper Limit in Highest $P_T$ Bin}

\begin{center}
\epsfig{file=r4.eps}
\end{center}

Examine the \Red{one-sided upper limit:}
\tiny
\begin{equation}
P=\frac{R_4^{\mathrm{true}}-R_4^{\mathrm{meas}}}{\sigma^+}, \nonumber
\end{equation}

\begin{itemize}
\item Expect that $P>1$ will occur 16\% of the time
\item Observe 17.5\% 
\end{itemize}

\pagebreak

\tit{Confidence Level Interval on $R_4$}

Obtain \Red{$R_4^{\mathrm{fit}}=0$} (fraction of top with $P_T>225$~\GeVc)
\tiny
\begin{itemize}
	\item Set a 95\%\ CL limit using a MC technique
	\begin{itemize}
		\item Analyze samples of MC events with varying $R_4^{\mathrm{true}}$. 
		\item Smear $R_4^{\mathrm{true}}$ in each with
		Gaussian distribution with a width equal to 
		systematic uncertainty
		\item Determine value of $R_4^{\mathrm{true}}$ where 
		only 5\% of the pseudo experiments have $R_4^{\mathrm{fit}}=0$
\\[0.03in]
	\end{itemize}
\end{itemize}

\tiny
\begin{center}
CDF PRELIMINARY\\
\begin{tabular}{|c|c|}
\hline
Systematic Effect & $\delta(R_4)$ \\
\hline
Background Model & $\pm 0.0028$ \\
Jet Energy Scale & ${}^{+0.0007}_{-0.0042}$ \\
No Initial State Radiation & $\pm 0.0045$ \\
Final State Radiation & $\pm 0.0095$ \\
Flat $P_T$ Spectrum & $\pm 0.0157$ \\
$m_t$ = 180~GeV & -0.0160 \\
\hline
\end{tabular}
\end{center}
\small

\pagebreak

\tit{95\% Confidence Level Upper Limit}

\begin{center}
\epsfig{file=find95.eps}
\end{center}

\vspace{0.25in}

\tiny
In agreement with result obtained by integrating under the likelihood
function. 

Without systematics, $R_4 < 0.109$ at 95\% CL

\pagebreak

\tit{Magnitude of Various Systematics}

\begin{center}
\epsfig{file=syst.eps}
\end{center}

\tiny
\begin{center}
CDF PRELIMINARY
\begin{tabular}{|c|ccccc|}
\hline
\hline
Syst. & $\delta R_1$ & $\delta R_2$ & $\delta R_3$ & $\delta R_4$ &$ \delta (R_1+R_2)$\\
\hline
$m_t$ & ${}^{+0.026}_{-0.000}$ & ${}^{+0.00}_{-0.027}$ &
${}^{+0.023}_{-0.000}$& ${}^{+0.000}_{-0.018}$& ${}^{+0.006}_{-0.012}$ 
\\
ISR & $\pm 0.016$ & $\pm 0.011 $& $\pm 0.005 $& $\pm 0.005$ &$\pm 0.007$\\
FSR & $\pm 0.038$ & $\pm 0.023 $& $\pm 0.010 $& $\pm 0.005$& $\pm 0.015$\\
JES & ${}^{+0.020}_{-0.028}$& ${}^{+0.037}_{-0.006}$& ${}^{+0.000}_{-0.008}$& ${}^{+0.000}_{-0.003}$& ${}^{+0.014}_{-0.000}$\\
$Q^2$ & $\pm 0.025$& $\pm 0.008$& $\pm 0.008$& $\pm 0.010$ & $\pm
0.016$ \\
$P_T$ & $\pm 0.032$& $\pm 0.045$& $\pm 0.055$& $\pm 0.016$& $\pm 0.036$ \\
Acceptance  & ${}^{+0.010}_{-0.023}$& ${}^{+0.013}_{-0.012}$& ${}^{+0.016}_{-0.014}$& ${}^{+0.000}_{-0.000}$& ${}^{+0.025}_{-0.011}$\\
\hline
\hline
\end{tabular}
\end{center}

\small

\pagebreak

\begin{center}
\Red{Top Quark Differential Cross Section}
\end{center}
\small
\begin{eqnarray}
R_1+R_2 & = & 0.72^{+0.13}_{-0.13}\mathrm{(stat)}
^{+0.06}_{-0.06}\mathrm{(syst)}\nonumber \\
R_4 & < & 0.114~\mathrm{at~95\%~C.L.}  \nonumber
\end{eqnarray}
\begin{center}
\epsfysize=4.0in
\epsffile{sm.eps}
\end{center}
\tiny
\begin{center}
\begin{tabular}{|c|l|}
\hline
$P_T$ Bin & Measured Fraction of Top Quarks \\
\hline
$0<P_T<75$~GeV/c & $R_1 = 0.29^{+0.18}_{-0.18}\mathrm{(stat)}
^{+0.08}_{-0.08}\mathrm{(syst)}$\\
$75<P_T<150$~GeV/c & $R_2= 0.42^{+0.18}_{-0.18}\mathrm{(stat)}
^{+0.05}_{-0.07}\mathrm{(syst)}$\\
$150<P_T<225$~GeV/c & $R_3= 0.29^{+0.12}_{-0.10}\mathrm{(stat)}
^{+0.06}_{-0.05}\mathrm{(syst)}$\\
$225<P_T<300$~GeV/c & $R_4=0.000^{+0.035}_{-0.000}\mathrm{(stat)}
^{+0.019}_{-0.000}\mathrm{(syst)}$\\
\hline
\end{tabular}
\end{center}

\pagebreak

\tit{Acceptance Calculations}

\vspace{0.5in}

\Red{Question:} Are selection criteria/triggers biased in $P_T$?
\tiny
\begin{itemize}
\item Generate large HERWIG+QFL$^\prime$ samples, each constrained to
have top quarks coming from one $P_T$ bins, and count the
fraction of events that pass cuts
\item Only interested in \Red{Relative} acceptance for each bin 
\item Estimate systematic uncertainty by recomputing results
for most important systematic errors
\end{itemize}

\begin{center}
\epsfig{file=relaccep.eps}
\end{center}

\pagebreak

\tit{Unsmearing Methodology}

Break the data sample up into two subsamples and perform an
\Red{unbinned likelihood fit} to the data

\tiny
\begin{itemize}
\item No Tag Hadronic (k=1)
\item Tagged Hadronic (k=2)
\end{itemize}

\tiny
Then perform simultaneous maximization of the following
likelihood function in each of the tagging subsamples:

\begin{equation}
-\ln[{\cal L}_k] =\sum_{i=1}^{n_{data}} -\ln \left [
(1-B_k)\sum_{j=1}^{n_{bin}} R_j
T_{jk}(P_T^i) + B_k V(P_T^i) \right ]
\end{equation}

\tiny
\begin{itemize}
\item $R_i$ is the fraction of top quarks produced in true bin $i$
\item $B_1$ is the background fraction in the untagged events.
\item $B_2$ is the background fraction in the tagged events.
\item The $T_k$, $V$ are the response functions for the signal and
background, respectively.
\end{itemize}

\small
The signal ($T_{jk}(P_T)$) and background ($V(P_T)$) response functions
are normalized to unity.

The $B_i$ are constrained via Gaussian probability distributions about
the background estimates.

\pagebreak

\tit{The Bootstrap}

\tiny
\begin{itemize}
	\item Methodology appears to be reasonably successful
	\item However, have overlooked one potential problem
	\item A given set of response functions is only valid for a particular
	assumption about how the $P_T$ distribution varies \Red{within each
	true $P_T$ bin!}
\end{itemize}

\small
Thus, we bootstrap:
\begin{center}
\epsfig{file=bts.eps}
\end{center}

\tiny
After each iteration, perform rejection against new true $P_T$
distribution to generate next set of response functions

\pagebreak
%
%  Wrap up
%
\tit{Summary}

\small
Our work on top using Run I data coming to close
\tiny
\begin{itemize}
	\item Will complete $P_T$\ measurements
	\item Have $W^\prime \rightarrow t\bar{b}$\ analysis underway
	\item Would like to complete branching fraction study
			\\[0.1in]
\end{itemize}

\small
All this sets the stage for Run II
\tiny
\begin{itemize}
	\item Will start data taking sometime in 2000 (April-Sep?)
	\item Run for 2-4 years, with goal to collect $\sim2$~\invfb
	\item Increase top quark sample $\times 50$
			\\[0.1in]
\end{itemize}

\small
By the time ATLAS turns on,
\tiny
\begin{itemize}
	\item Top will be well-studied
	\begin{itemize}
		\item Understood as a background
	\end{itemize}
	\item We will be able to focus on those properties that
	are most crucial to extending our understanding of 
	elementary particles
\end{itemize}

\end{document}
