We present a measurement of the mass of the top quark. Our event sample is selected from proton-antiproton collisions, at 1.96 TeV center-of-mass energy, observed with the CDF detector at Fermilab's Tevatron. We consider a 318 pb$^{-1}$ dataset collected between March 2002 and August 2004. We select events that contain one energetic lepton, large missing transverse energy, exactly four energetic jets, and at least one displaced vertex $b$ tag. Our analysis uses leading-order $t\bar{t}$ and background matrix elements along with parameterized parton showering to construct event-by-event likelihoods as a function of top quark mass. From the 63 events observed with the 318 pb$^{-1}$ dataset we extract a top quark mass of $172.0 \pm 2.6$ (stat) $\pm 3.3$ (syst) GeV$/c^2$ from the joint likelihood. The mean expected statistical uncertainty is 3.2 GeV$/c^2$ for $m_t = 178$ GeV$/c^2$ and 3.1 GeV$/c^2$ for $m_t = 172.5$ GeV$/c^2$. The systematic error is dominated by the uncertainty of the jet energy scale. Posted to /cdf/pub/thesis/cdf8645_GibsonThs_MT_LJ_ME.ps http://www-cdf.fnal.gov/thesis/cdf8645_GibsonThs_MT_LJ_ME.ps Posted by agibson