We determine the weak interaction corrections of order αₛ²α to hadronic top-quark pair production. First we compute the one-loop weak corrections to tt̄ production due to gluon fusion and the order αₛ²α corrections to tt̄ production due to (anti)quark-gluon scattering in the standard model. With our previous result [W. Bernreuther, M. F\"ucker, and Z. G. Si, Phys. Lett. B 633, 54 (2006).] this yields the complete corrections of order αₛ²α to $gg$, qq̄, $qg$, and q̄g induced hadronic tt̄ production with t and t̄ polarizations and spin correlations fully taken into account. For the Tevatron and the LHC we determine the weak contributions to the transverse top momentum and to the tt̄ invariant-mass distributions. At the LHC these corrections can be of the order of 10% compared with the leading-order results, for large pT and Mtt̄, respectively. Apart from parity-even tt̄ spin correlations we analyze also parity-violating double- and single-spin asymmetries and show how they are related if $CP$ invariance holds. For t (and t̄) quarks which decay semileptonically, we compute a resulting charged-lepton forward-backward asymmetry APV with respect to the t (t̄) direction, which is of the order of 1% at the LHC for suitable invariant-mass cuts.
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Bernreuther et al. (2006) studied this question.