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
$5.4~ ext{fb}^{-1}$ 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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