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The contributions of $G'$-boson predicted by the chiral color symmetry of quarks to the cross section $\sigma_{t\bar{t}}$ and to the forward-backward asymmetry $A_{\rm FB}^{p \bar p}$ of $t\bar{t}$ production at the Tevatron are calculated with account of the difference of the strengths of the $\bar q q G$ and $\bar q q G'$ interactions.
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