We report on a search for a spin-zero non-standard-model particle in proton-antiproton collisions collected by the Collider Detector at Fermilab at a center-of-mass-energy of 1.96 TeV. This particle, the $phi$ boson, is expected to decay into a bottom-antibottom quark pair and to be produced in association with at least one bottom quark. The data sample consists of events with three jets identified as initiated by bottom quarks and corresponds to $5.4~text{fb}^{-1}$ of integrated luminosity. In each event, the invariant mass of the two most energetic jets is studied by looking for deviations from the multijet background, which is modeled using data. No evidence is found for such particle. Exclusion upper limits ranging from 20 to 2 pb are set for the product of production cross sections times branching fraction for hypothetical $phi$ boson with mass between 100 and 300 GeV/$c^2$. These are the most stringent constraints to date.
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