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We measure the forward--backward asymmetry of the production of top quark andantiquark pairs in proton-antiproton collisions at center-of-mass energy$\sqrt{s} = 1.96~\mathrm{TeV}$ using the full data set collected by theCollider Detector at Fermilab (CDF) in Tevatron Run II corresponding to anintegrated luminosity of $9.1~\rm{fb}^{-1}$. The asymmetry is characterized bythe rapidity difference between top quarks and antiquarks ($\Delta y$), andmeasured in the final state with two charged leptons (electrons and muons). Theinclusive asymmetry, corrected to the entire phase space at parton level, ismeasured to be $A_{\text{FB}}^{t\bar{t}} = 0.12 \pm 0.13$, consistent with theexpectations from the standard-model (SM) and previous CDF results in the finalstate with a single charged lepton. The combination of the CDF measurements ofthe inclusive $A_{\text{FB}}^{t\bar{t}}$ in both final states yields$A_{\text{FB}}^{t\bar{t}}=0.160\pm0.045$, which is consistent with the SMpredictions. We also measure the differential asymmetry as a function of$\Delta y$. A linear fit to $A_{\text{FB}}^{t\bar{t}}(|\Delta y|)$, assumingzero asymmetry at $\Delta y=0$, yields a slope of $\alpha=0.14\pm0.15$,consistent with the SM prediction and the previous CDF determination in thefinal state with a single charged lepton. The combined slope of$A_{\text{FB}}^{t\bar{t}}(|\Delta y|)$ in the two final states is$\alpha=0.227\pm0.057$, which is $2.0\sigma$ larger than the SM prediction.

Measurement of the forward-backward asymmetry of top-quark and antiquark pairs using the full CDF Run II data set