  We describe a measurement of the top quark mass from events produced in
proton-antiproton collisions at a center-of-mass energy of 1.96 TeV, using the
Collider Detector at Fermilab. We identify top-antitop candidates where both W
bosons from the top quarks decay into leptons (electron, muon, or tau plus
neutrino) from a data sample of 360 inverse picobarns. The top quark mass is
reconstructed in each event separately by three different methods, which draw
upon simulated distributions of the neutrino pseudorapidity, top-antitop
longitudinal momentum, or neutrino azimuthal angle in order to extract
probability distributions for the top quark mass. For each method,
representative mass distributions, or templates, are constructed from simulated
samples of signal and background events, and parameterized to form continuous
probability density functions. A likelihood fit incorporating these
parameterized templates is then performed on the data sample masses in order to
derive a final top quark mass. Combining the three template methods, taking
into account correlations in their statistical and systematic uncertainties,
results in a top quark mass measurement of 170.1 +/- 6.0 (stat) +/- 4.1 (syst)
GeV/c^2.
