We present a measurement of the mass difference between top ($t$) and
anti-top ($ar{t}$) quarks using $tar{t}$ candidate events reconstructed in
the final state with one lepton and multiple jets. We use the full data set of
Tevatron $sqrt{s} = 1.96$ TeV proton-antiproton collisions recorded by the CDF
II detector, corresponding to an integrated luminosity of 8.7 fb$^{-1}$. We
estimate event-by-event the mass difference to construct templates for
top-quark signal events and background events. The resulting mass difference
distribution of data compared to signal and background templates using a
likelihood fit yields $Delta M_{top} = {M}_{t} - {M}_{ar{t}} = -1.95 $pm$
1.11 (stat) $pm$ 0.59 (syst)$ and is in agreement with the standard model
prediction of no mass difference.
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