  We analyze the impact of effective axial-vector coupling of the gluon on spin
polarization observables in $t\bar{t}$ pair production at the LHC. Working at
leading order in QCD, we compute the $t\bar{t}$ spin-correlation and left-right
spin asymmetry coefficients in the helicity basis in the laboratory frame as
functions of the new physics scale $\Lambda$ associated with this coupling. We
found that the $t\bar{t}$ invariant mass dependent asymmetries are more
sensitive to the scale $\Lambda$ than the corresponding inclusive ones, in
particular when suitable cuts selecting high $t\bar{t}$ invariant mass regions
are imposed. In the context of this scenario, we show that the LHC has
potential either to confirm or to rule out the Tevatron FB top asymmetry
anomaly by analyzing the $t\bar{t}$ spin-correlation and left-right
polarization asymmetries. On the other hand, stringent lower bound on the new
physics scale $\Lambda$ can be set in this scenario if no significant
deviations from the SM predictions for those observables will be measured.
