  We obtain a soft plus virtual approximation to the NNLO QCD contributions to
the top-pair invariant mass distribution at hadron colliders. It is valid up to
corrections of order m_t^2/M^2, with M the pair invariant mass. This is
currently the most complete QCD calculation for a differential cross section in
top-quark pair production, and is useful for describing the high invariant mass
region characteristic of boosted top quarks. We use our results to construct an
improved NNLO approximation for the pair invariant mass distribution and
compare it with previous, less complete approximations based on logarithmic
terms from NNLL soft-gluon resummation alone. We find that the new NNLO
approximation produces moderate enhancements of the differential cross section
compared to previous ones, the effect being slightly more important at low
values of invariant mass than at high ones. On the other hand, at high values
of invariant mass the new NNLO corrections are dominated by even higher-order
effects included in NNLL soft-gluon resummation, reaffirming the need for
resummation in describing the highly boosted regime.
