  We report an updated measurement of the top quark mass obtained from ppbar
collisions at sqrt(s) = 1.96 TeV at the Fermilab Tevatron using the CDF II
detector. Our measurement uses a matrix element integration method to obtain a
signal likelihood, with a neural network used to identify background events and
a likelihood cut applied to reduce the effect of badly reconstructed events. We
use a 2.7 fb^-1 sample and observe 422 events passing all of our cuts. We find
m_t = 172.2 +/- 1.0 (stat.) +/- 0.9 (JES) +/- 1.0 (syst.) GeV/c^2, or m_t =
172.2 +/- 1.7 (total) GeV/c^2.
