Speaker: Colomba Brancaccio (MPP Munich)

Top-quark pair production in association with a jet, a photon or a Higgs boson is of high priority in the LHC precision programme, and matching the precision of the experimental data requires predictions at NNLO in QCD. In this talk I review recent progress on tt̄+X at this accuracy. I first discuss tt̄H production in the framework of perturbative fragmentation functions. The latter describe the nearly collinear emission of a Higgs boson from a top quark and reproduce the leading mass dependence of the exact NLO calculation, while the extension to NNLO introduces nontrivial subtleties and complications. I then turn to tt̄j, where the two-loop five-point amplitudes have long been the bottleneck towards NNLO predictions for this process. I present their leading-colour computation: the finite remainder is reconstructed analytically from finite-field evaluations using a tailored set of special functions evaluated through numerical integration of its differential equations. This result has made NNLO QCD predictions for the pp->tt̄j cross section and differential distributions possible. Finally, I show how the same techniques apply to the planar two-loop integrals relevant for tt̄γ hadroproduction at leading-colour, as a first step towards the NNLO computation of this process.