  We report a measurement of the top quark mass, m_t, obtained from ppbar
collisions at sqrt(s) = 1.96 TeV at the Fermilab Tevatron using the CDF II
detector. We analyze a sample corresponding to an integrated luminosity of 1.9
fb^-1. We select events with an electron or muon, large missing transverse
energy, and exactly four high-energy jets in the central region of the
detector, at least one of which is tagged as coming from a b quark. We
calculate a signal likelihood using a matrix element integration method, with
effective propagators to take into account assumptions on event kinematics. Our
event likelihood is a function of m_t and a parameter JES that determines /in
situ/ the calibration of the jet energies. We use a neural network discriminant
to distinguish signal from background events. We also apply a cut on the peak
value of each event likelihood curve to reduce the contribution of background
and badly reconstructed events. Using the 318 events that pass all selection
criteria, we find m_t = 172.7 +/- 1.8 (stat. + JES) +/- 1.2 (syst.) GeV/c^2.
