  The Standard Model of particle physics contains about two dozen parameters -
such as particle masses - whose origins are still unknown and cannot be
predicted, but whose values are constrained through their interactions. In
particular, the masses of the top (t) quark (M_t) and W boson constrain the
mass of the long-hypothesized, but thus far not observed, Higgs boson. A
precise measurement of the top-quark mass can therefore point to where to look
for the Higgs, and indeed whether the hypothesis of a SM Higgs is consistent
with experimental data. Since top quarks are produced in pairs and decay in
only ~10^-24 s into various final states, reconstructing their mass from their
decay products is very challenging. Here we report a technique that extracts
far more information from each top-quark event and yields a greatly improved
precision on the top mass of 5.3 GeV/c^2, compared to previous measurements.
When our new result is combined with our published measurement in a
complementary decay mode and with the only other measurements available, the
new world average for M_t becomes 178.0 +- 4.3 GeV/c^2. As a result, the most
likely Higgs mass increases from the experimentally excluded value of 96
GeV/c^2 to 117 GeV/c^2, which is beyond current experimental sensitivity. The
upper limit on the Higgs mass at 95% confidence level is raised from 219
GeV/c^2 to 251 GeV/c^2.
