\title{Top Quark Mass Measurement Using the Template Method in the
Lepton + Jets Channel at CDF II \\ \vspace*{2.0cm}}
\author{The CDF Collaboration}
\affiliation{URL http://www-cdf.fnal.gov}
\date{\today}

\begin{abstract}
This report presents a measurement of the top quark mass using
the CDF \runii detector at Fermilab.
Colliding beams of protons and anti-protons at Fermilab's
Tevatron ($\sqrt{s}=\tev{1.96}$) produce
top/anti-top pairs, which decay to $W^+W^-\bbbar$; events are
selected where one $W$ decays hadronically, and one $W$ decays
to either $e$ or $\mu$ plus a neutrino.
%
The data sample was collected between
March 2002 and September 2003, and corresponds to an integrated
luminosity of $\invpb{318}$.
One hundred and thirty-five candidate \ttbar events are separated into
four subsamples based on jet transverse energy thresholds and the number
of $b$ jets identified by a displaced vertex.
%
In each event, the best fit top quark invariant mass is determined
by minimizing a \chisq for the overconstrained kinematic system.  At the
same time, the hadronically decaying $W$ boson is reconstructed in the same
event sample.  The comparison of the precisely known and observed $W$ boson 
mass provides an independent {\it in situ}\ determination of the energy 
scale of the hadronic jets.
A simultaneous likelihood fit of the reconstructed top quark masses and
the $W$ boson invariant masses in the data sample to distributions from
simulated signal and background events gives a top mass of
$\gevcc{\measAStatSyst{173.5}{3.7}{3.6}{1.7}}$.  This technique provides
a 22\%\ reduction in the uncertainty in the jet energy scale, the
dominant systematic uncertainty in this measurement.  This is the most
precise single measurement of the top quark mass.
%
A measurement made without the simultaneous constraint on the {\it in situ}\ 
jet energy
scale calibration yields a consistent top quark mass value of 
$\gevcc{measAStatSyst{173.2}{2.9}{2.8}{3.4}}$..
\end{abstract}

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\maketitle

\newpage
\section{Introduction}
\label{sec:intro}

A precision measurement of the top quark mass is one of the primary
goals of the upgraded Tevatron accelerator and its two general-purpose
detectors. In addition to being a fundamental parameter of the Standard
Model, the large top quark mass may indicate a special role for the
top quark in electroweak symmetry breaking. Due to the top quark's large
contribution to radiative corrections, a more accurate measurement will
make precision tests of the Standard Model more powerful, and provide
tighter constraints on the mass of the putative Higgs particle.

This article reports a measurement of the top quark mass in the
lepton + jets decay channel using the CDF detector at Fermilab,
with $\invpb{318}$ of collision data collected in \runii, between
March 2002 and August 2004.
A brief overview of the analysis is as follows. We scrutinize the
data for events where a \ttbar pair has been produced and has
decayed to two $W$ bosons and two $b$ quarks, where subsequently
one $W$ boson decayed to two quarks, and the other $W$ boson
decayed to an electron or muon and a neutrino. Thus we look for
a high-energy isolated electron or muon, missing energy representing the
neutrino, two jets of particles corresponding to the $b$ quarks,
and two additional jets corresponding to the hadronic $W$ decay.

We determine the mass of the top quark using a single quantity, the 
reconstructed top quark mass attempting a full-reconstruction of both top 
quark candidates in each event.  This quantity is
strongly dependent on the top quark pole mass.
We compare the distribution of the reconstructed mass from events in the 
data with the distributions derived
from events randomly generated and simulated at various values of
the top mass. We also simulate events from the expected background
processes. The top quark mass whose simulated events, when combined
with the background, best describe the distribution in the data,
is our measured value. We improve the power of the method
by separating the events into four subsamples that have different
background contamination and different sensitivity to the top mass.

For the quantity to be compared between data and simulated events,
we choose the reconstructed top quark mass, determined in each
event by minimizing a \chisq expression for the resolutions and
kinematic relationships in the \ttbar system. The mass reconstruction
is complicated by the fact that we don't know which jet represents
each quark in the event. However, since we know something about the
intermediate states of the \ttbar system, such as the
$W$ mass, the system is overconstrained, and we can choose which
jet to assign to which quark based on the fit quality.

The dominant systematic uncertainty in this measurement arises from the
determination of the jet energy scale for the top quark daughter jets, the
two b-quarks in the event and the two jets from the $W$ boson decay.  We
have developed a technique to use the fact that the $W$ boson daughters
should form a dijet invariant mass that is consistent with the precisely
know $W$ boson.  We show that this jet energy scale information is
largely independent of the top quark mass, and can be used to
significantly reduce the uncertainties in the overall top quark mass
measurement.
We also make a measurement of the top quark mass without this additional
information and obtain consistent results.  

The method used is similar in spirit to an analysis
performed at CDF using data from \runi~\cite{Affolder:2000vy}.
Combined with other analyses that use more sophisticated
techniques~\cite{Abazov:2004cs,r_run2dlm},
this approach has several advantages. First, many parts of the detector,
as well as all of the offline software, are new with respect to \runi.
By performing an analysis similar to the one previously published,
we can draw on the experience and expertise developed
in \runi and gain confidence in our \runii tools and methods.
Second, this analysis is based on kinematic reconstruction of the top
quark final state, and as such makes fewer assumptions than methods based
on the full Standard Model matrix element for \ttbar production and decay.
Finally, this measurement can be combined with measurements using
the other techniques, so that we can take full advantage of
non-overlapping statistical and systematic uncertainties.

