We determine the weak interaction corrections of order ${\alpha }_s^2\alpha$ to hadronic top-quark pair production. First we compute the one-loop weak corrections to $t\overline{t}$ production due to gluon fusion and the order ${\alpha }_s^2\alpha$ corrections to $t\overline{t}$ production due to (anti)quark-gluon scattering in the standard model. With our previous result [W. Bernreuther, M. Fücker, and Z. G. Si, Phys. Lett. B 633, 54 (2006).] this yields the complete corrections of order ${\alpha }_s^2\alpha$ to $gg$, $q\overline{q}$, $qg$, and $\overline{q}g$ induced hadronic $t\overline{t}$ production with $t$ and $\overline{t}$ 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 $t\overline{t}$ invariant-mass distributions. At the LHC these corrections can be of the order of 10% compared with the leading-order results, for large $p_T$ and $M_{t\overline{t}}$, respectively. Apart from parity-even $t\overline{t}$ 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 $\overline{t}$) quarks which decay semileptonically, we compute a resulting charged-lepton forward-backward asymmetry $A_{PV}$ with respect to the $t$ ($\overline{t}$) direction, which is of the order of 1% at the LHC for suitable invariant-mass cuts.

• Received 26 October 2006

DOI:https://doi.org/10.1103/PhysRevD.74.113005