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%	12 Jul 05	PKS	First Draft
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%       13 Jul 05       EMB     Cleanup and add plots
%       16 Jul 05       PKS     Tighten down and revise based on comments
%       20 Jul 05       PKS     Incorporate 2nd draft comments.
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The top quark is the heaviest known elementary particle with a mass
40 times that of the next-heaviest quark or lepton.
Because of this comparatively large mass, 
top quark studies provide insight into our understanding of mass in
general, and test theories that explain the large range of quark
and lepton masses.
Within the context of the 
Standard Model of particle physics, 
the top quark mass is related to the masses
of the $W$ boson and the Higgs boson, the latter
object being the key to our understanding of the origin of 
mass~\cite{r_electroweakfit}.
Precision measurements of the top quark and $W$ boson masses 
test the consistency of the Standard Model, and in particular the Higgs
mechanism. 
An improved measurement of the top quark mass is therefore 
a main goal of the experiments at the Fermilab Tevatron collider.

In this Letter we present two measurements of the top quark mass in the
lepton + jets decay channel.
We use a sample of \ttbar\ decays corresponding to
\invpb{318} of proton-antiproton collisions at $\sqrt{s}=1.96$\ TeV 
and collected 
using the Collider Detector at Fermilab
(CDF II) between February 2002 and August 2004.
In the lepton + jets channel, \ttbar pair production is followed by
the decay of each top quark to a $W$ boson and a $b$ quark, the
hadronic decay of one $W$\ boson, and the leptonic decay of the other.
This decay channel has the largest branching fraction with good 
signal-to-background, allowing accurate top quark mass measurements.
Events in this channel contain an electron or muon and a neutrino
from the leptonic $W$ boson decay, two quark jets from the hadronic
$W$ boson decay, and two $b$-quark jets.

We select events consistent with this decay topology and analyze
them using two complementary methods.  Both methods have a top quark mass
 accuracy 30\%\ greater than earlier results, and have 
different statistical and systematic uncertainties.
The first method uses an
event-by-event likelihood analysis employing the full matrix element
for \ttbar production and decay to extract a joint likelihood as a
function of the top quark mass, \mtop.
This technique, known as the ``dynamical likelihood method'' or DLM,
was developed by the CDF collaboration~\cite{Kondo:1988yd} and 
is similar to that used by the \DZero collaboration to make the 
previous most precise measurement of the top quark mass~\cite{Abazov:2004cs}.
A second method, developed by the CDF
collaboration~\cite{r_evidence_prd}, reconstructs a top quark
mass, \mreco, in each event and compares the distribution of \mreco\
with template distributions derived from
model calculations to estimate \mtop.
We have improved this ``template method'' 
by using the fact that the hadronically decaying $W$ boson daughters
should form a final state whose invariant mass is consistent with 
the known $W$ boson mass.  This allows us to constraint the dominant
systematic uncertainty in earlier measurements, the jet energy scale.

%
%  Overview of Experiment, data selection and contamination
%
The CDF II detector 
\cite{r_cdfDetector_coord}\
is a general-purpose charged and neutral particle
detector located at an interaction point along the
Tevatron collider.
%and is described in detail 
%elsewhere~
%~\footnote{We employ a cylindrical coordinate
%system where $\theta$ is the polar angle with respect to the proton
%beam, $\phi$ is the azimuthal angle, and pseudorapidity is 
%$\eta = -\ln\tan(\theta/2)$.  Transverse energy and momentum are 
%$E_T= E\sin\theta$ and $p_T=p\sin\theta$, respectively, where $E$ and
%$p$ are energy and momentum. Missing transverse energy is
%$|-\Sigma_{i}\et^{i}\mathbf{n_{i}}|$,
%where $\mathbf{n_{i}}$ is the unit vector in the transverse plane
%that points from the beamline to the $i$th calorimeter tower.}.
The detector comprises a solenoidal charged particle spectrometer, consisting of 
an eight-layer silicon microstrip detector array and a cylindrical drift
chamber immersed in a 1.4 T magnetic field, a
segmented sampling calorimeter with acceptance
up to pseudorapidity $|\eta|=3.6$,
and a set of charged particle detectors outside the
calorimeter used to identify muon candidates.

Events for this analysis were selected by the presence of an
electron or muon candidate with transverse momentum
$\pt>\gevc{20}$ and $|\eta|<1$\ and missing
transverse energy exceeding \gev{20}, corresponding to a
high-energy neutrino candidate.  
The signal-to-background was improved by requiring in each event the
presence of four or more jets with $|\eta|<2.0$. 
To reduce backgrounds further
we required either (a) at least four jets with transverse energy 
$\et>\gev{21}$\ or (b) at least three jets with $\et>\gev{15}$\ and
a fourth jet with $\et>\gev{8}$\ with at least
one jet identified as a $b$ quark candidate through the presence of 
a displaced vertex within
the jet arising from the decay of the long-lived bottom 
quark ($b$ tag).
This selection resulted in 165 events that, based on our
background estimates, are primarily \ttbar events.
The methods used to estimate the backgrounds are detailed
in~\cite{r_run2topxsec}.

The DLM analysis uses a subset of those data and selects events containing only
four jets with $\et>\gev{15}$ where at least one of the jets has
a $b$ tag. This results in 63 events.
We have estimated the various sources of background contamination in this 
sample, summarized in \Tab{t:backgroundnumber}, to be
$9.2\pm1.8$\ events.
The template method subdivides the 165 events into four non-overlapping
subsamples with 
different expected \mreco distributions and background levels.
Ordered by decreasing statistical power, the subsamples are
1) events with at least four jets with $\et>\gev{15}$ and one $b$-tagged jet
(``1-tag Tight'' sample with 63 events),
2) events with two $b$-tagged jets
(``2-tag'' sample with 25 events),
3) events with a fourth jet with $\gev{8}<\et<\gev{15}$ and one $b$-tagged jet
(``1-tag Loose'' sample with 33 events), and
4) events with four jets with $\et>\gev{21}$ and no $b$-tagged jets
(``0-tag'' sample with 44 events).
The estimated background levels in the samples with a $b$ tag are 
summarized in \Tab{t:backgroundnumber}.
The background level in the 0-tag sample is determined in the subsequent fit.

\begin{table}
\caption[Sample composition.]
{The background composition and the number of \ttbar
candidates for events with $\geq1$ $b$ tag, and
for the subset of them used in the DLM analysis.}
\label{t:backgroundnumber}
\begin{ruledtabular}
\begin{tabular}{lcc}
                         & $\geq1$ $b$ tag & DLM sample \\
\hline
Source & \multicolumn{2}{c}{Expected Background} \\
\cline{2-3}
$W$ + jets          & \measErr{19.6}{2.4} & \measErr{5.3}{1.1} \\
QCD                 & \measErr{4.7}{0.7} & \measErr{3.1}{1.0} \\
Other               & \measErr{2.3}{0.2} & \measErr{0.8}{0.1} \\
\hline
Total               & \measErr{26.6}{3.0} & \measErr{9.2}{1.8} \\
\hline\hline
& \multicolumn{2}{c}{Identified \ttbar Candidates} \\
\cline{2-3}
Data                &  121 & 63 \\
\end{tabular}
\end{ruledtabular}
\end{table}

Both analyses use calibrated jet energies, based on
a combination of instrumental calibration and
analysis of data control samples~\cite{r_NIMJES}.
The uncertainty on the jet energy scale 
$\sigma_c$\ is the major source of systematic uncertainty on
\mtop. For jets in the \ttbar sample, $\sigma_c$ is roughly
3\% of the measured jet energy, depending on the $\eta$ and \pt of the jet.
The parameter \jes is defined as the difference between our measured jet energy
after calibration and the true jet energy
averaged over all jets in the sample, in units of $\sigma_c$.
