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Search for a heavy particle decaying to a top quark and a light quark in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV

We present a search for a new heavy particle $M$ produced in association with a top quark, $p\bar{p}\rightarrow t(M \rightarrow \bar{t}q)$ or $p\bar{p}\rightarrow \bar{t}(\bar{M}\rightarrow t\bar{q})$, where $q$ stands for up quarks and down quarks. Such a particle may explain the recent anomalous measurements of top-quark forward-backward asymmetry. If the light-flavor quark ($q$) is reconstructed as a jet ($j$), this gives a $\bar{t}+j$ or $t+j$ resonance in $t\bar{t}$+jet events, a previously unexplored experimental signature. In a sample of events with exactly one lepton, missing transverse momentum and at least five jets, corresponding to an integrated luminosity of 8.7 fb$^{-1}$ collected by the CDF II detector, we find the data to be consistent with the standard model. We set cross-section upper limits on the production ($p\bar{p}\rightarrow Mt$ or $\bar{M}\bar{t}$) at 95% confidence level from 0.61 pb to 0.02 pb for $M$ masses ranging from 200 GeV$/c^2$ to 800 GeV$/c^2$, respectively.