NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels

This is a second paper in our ongoing calculation of the next-to-next-to-leading order (NNLO) QCD correction to the total inclusive top-pair production cross-section at hadron colliders. In this paper we calculate the reaction $q\bar q \to t\bar t + q\bar q$ which was not considered in our previous work on $q\bar q \to t\bar t +X$ due to its phenomenologically negligible size. We also calculate all remaining fermion-pair-initiated partonic channels $qq', q\bar q'$ and $qq$ that contribute to top-pair production starting from NNLO. The contributions of these reactions to the total cross-section for top-pair production at the Tevatron and LHC are small, at the permil level. The most interesting feature of these reactions is their characteristic logarithmic rise in the high energy limit. We compute the constant term in the leading power behavior in this limit, and achieve precision that is an order of magnitude better than the precision of a recent theoretical prediction for this constant. All four partonic reactions computed in this paper are included in our numerical program Top++. The calculation of the NNLO corrections to the two remaining partonic reactions, $qg\to t\bar t+X$ and $gg\to t\bar t+X$, is ongoing.