Mixed QCD and weak corrections to top quark pair production at hadron colliders

The order ${\alpha }_s^2\alpha$ mixed QCD and weak corrections to top quark pair production by quark antiquark annihilation are computed, keeping the full dependence on the $t$ and $\bar{t}$ spins. We determine the contributions to the cross section and to single and double top spin asymmetries at the parton level. These results are necessary ingredients for precise standard model predictions of top quark observables, in particular of top spin-induced parity-violating angular correlations and asymmetries at hadron colliders.