  We present the first complete next-to-next-to-leading order (NNLO) QCD
predictions for differential distributions in the top-quark pair production
process at the LHC. Our results are derived from a fully differential partonic
Monte Carlo calculation with stable top quarks which involves no approximations
beyond the fixed-order truncation of the perturbation series. The NNLO
corrections improve the agreement between existing LHC measurements [V.
Khachatryan et al. (CMS Collaboration), Eur. Phys. J. C 75, 542 (2015)] and
standard model predictions for the top-quark transverse momentum distribution,
thus helping alleviate one long-standing discrepancy. The shape of the
top-quark pair invariant mass distribution turns out to be stable with respect
to radiative corrections beyond NLO which increases the value of this
observable as a place to search for physics beyond the standard model. The
results presented here provide essential input for parton distribution function
fits, implementation of higher-order effects in Monte Carlo generators as well
as top-quark mass and strong coupling determination.
