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The high luminosity that will be accumulated at the LHC will enable precisedifferential measurements of the hadronic production of a top--antitop-quarkpair in association with a $\text{W}$ boson. Therefore, an accurate descriptionof this process is needed for realistic final states. In this work we combinefor the first time the NLO QCD and electroweak corrections to the fulloff-shell $\text{t}\overline{\text{t}}{\text{W}}^+$ production at the LHC inthe three-charged-lepton channel, including all spin correlations, non-resonanteffects, and interferences. To this end, we have computed the NLO electroweakradiative corrections to the leading QCD order as well as the NLO QCDcorrections to both the QCD and the electroweak leading orders.

Combined NLO EW and QCD corrections to off-shell $\text{t}\overline{\text{t}}\text{W}$ production at the LHC