We report on a study of the dijet invariant-mass distribution in events with one identified lepton, a significant imbalance in the total event transverse momentum, and two jets. This distribution is sensitive to the possible production of a new particle in association with a $W$ boson, where the boson decays leptonically. We use the full data set of proton-antiproton collisions at 1.96 TeV center-of-mass energy collected by the Collider Detector at the Fermilab Tevatron and corresponding to an integrated luminosity of 8.9 fb$^{-1}$. The data are found to be consistent with standard-model expectations, and a 95$\%$ confidence level upper limit is set on the cross section for a $W$ boson produced in association with a new particle decaying into two jets.
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