Abstract
A brief summary of the calculation of the NLO QCD corrections to the process pp -> e+ ve mu- v_mu bb~ j + X is reported. This provides a complete description of the process of t-tbar + jet production with leptonic decays beyond the narrow-width approximation. Off-shell effects for top quarks and W boson decays are fully taken into account, namely all resonant and non-resonant contributions are included in the fixed-order calculation. Selected results for total and differential cross sections are shown for the case of the LHC Run I at the energy of 8 TeV.
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