  We report on a search for a dijet resonance in events with only two or three
jets and large imbalance in the total event transverse momentum. This search is
sensitive to the possible production of a new particle in association with a
$W$ or $Z$ boson, where the boson decays leptonically with one or more
neutrinos in the final state. We use the full data set collected by the CDF II
detector at the Tevatron collider at a proton-antiproton center-of-mass energy
of 1.96 TeV. These data correspond to an integrated luminosity of 9.1
fb$^{-1}$. We study the invariant mass distribution of the two jets with
highest transverse energy. We find good agreement between data and standard
model background expectations and measure the combined cross section for WW,
WZ, and ZZ production to be $13.8^{+3.0}_{-2.7}$ pb. No significant anomalies
are observed in the mass spectrum and 95% credibility level upper limits are
set on the production rates of a potential new particle in association with a
$W$ or $Z$ boson.
