NLO QCD corrections to off-shell ttj production at the LHC

A short summary of results for top-quark pair production in association with a jet with NLO QCD off-shell effects at the LHC is given. The calculation is based on the matrix element for the $pp \to e^+ \nu_e \mu^-\bar{\nu}_\mu b\bar{b} j$ process. All quantum effects are properly accounted for, which amounts to including all Feynman diagrams that result in this final state with interference effects as well as non-zero top-quark width effects. Results for total cross sections and a few differential distributions at the LHC Run1 energy of $\sqrt{s}=8$ TeV are presented. In addition, the size of top-quark off-shell effects is quantified for the total cross section in presence of rather inclusive cuts on all final states. Numerical results shown in this proceedings have been obtained with the HELAC-NLO Monte Carlo program.