\title{Top Quark Mass Measurement Using the Template Method in the
Lepton + Jets Channel at CDF II \\ \vspace*{2.0cm}}
\author{CDF Default Author List from February 2005 to July 2005}
\affiliation{http://www-cdf.fnal.gov/internal/spokes/Authors/tex/Author\_List\_Feb\_2005.ps}
\author{The CDF Collaboration}
\noaffiliation
\date{\today}

\begin{abstract}
This report presents a measurement of the top quark mass using
the \cdfii 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 corresponds to an integrated
luminosity of approximately \invpb{318}.
One hundred and sixty-five candidate \ttbar events are separated into
four subsamples based on jet transverse energy thresholds and the number
of $b$ jets identified by reconstructing a displaced vertex.
%
\note{The bit ``best fit top quark invariant mass'' is quite awkward.}
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 observed $W$ boson mass provides an \emph{in situ}
improvement of the determination of \jes, 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 quark mass of
\gevcc{\measAStatJESSyst{173.5}{3.7}{3.6}{1.5}}, or
\gevcc{\measAErr{173.5}{4.0}{3.9}}.
%Removed per Larry.
%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}{3.3}}.
%Finally, making use of an additional $b$ jet identification algorithm,
%we measure a top quark mass of
%\gevcc{\measAStatSyst{173.0}{2.9}{2.8}{3.3}}, also consistent with
%the primary result.
\end{abstract}

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\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 \note{(Should this be
CDF II?)} detector at Fermilab,
with $\invpb{318}$ of \ppbar collision data collected between
February 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.

Our measurement uses an observable that is strongly dependent on
the top quark pole mass, namely the reconstructed top quark mass.
This quantity is determined for each event by minimizing a \chisq
expression to perform a kinematic fit in the
\ttbar system~\cite{r_evidence_prd}. 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 each quark based on the fit quality. In addition,
some jets are experimentally identified as arising from $b$ quarks
using lifetime tagging, reducing the number of allowed assignments.

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 quark 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 quark mass.

\note{Stronger statement of this aspect per Doug?}
The dominant systematic uncertainty in this measurement arises from the
determination of the jet energy scale for the top quark daughter jets,
particularly the two jets from $b$ quarks.
To reduce this uncertainty,
we have developed a technique that uses the fact that the daughters
of the hadronically decaying $W$ boson
should form a dijet invariant mass that is consistent with
the precisely known $W$ boson mass.
We constrain the jet energy scale by comparing the distribution of
observed dijet invariant mass for the $W$ boson daughter jets with
the distributions expected for a $W$ boson decay assuming various
shifts in the jet energy scale.
We show that this improves the jet energy scale information
and is largely independent of the top quark mass.
Furthermore, since this information applies in large part to $b$ jets
as well, it can be used to significantly reduce the uncertainties
in the overall top quark mass measurement.
A measurement of the top quark mass without this additional
information gives consistent results, albeit with larger overall
uncertainties.

The method used is similar in spirit to an analysis performed at CDF
using data from \runi~\cite{Affolder:2000vy}.
Although other analyses are in progress using more sophisticated
techniques~\cite{Kondo:1988yd,Abazov:2004cs},
this approach has several advantages.
First, 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.
This is important since many parts of the detector,
as well as all of the offline software, are new with respect to \runi.
Second, this analysis is based on kinematic reconstruction of the
top quark final state, and as such is less sensitive to assumptions
about \ttbar production and decay than are methods based on the full
Standard Model matrix element.
Third, the \emph{in situ} determination of \jes is so far unique among
top quark mass analyses.
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.
