Full off-shell $t\bar{t}$ production in the semileptonic channel at the LHC

In this contribution, we summarize our results on the complete NLO predictions for the production of off-shell top quark pairs in the $\ell+j$ channel at the LHC. All NLO QCD and electroweak corrections are consistently included across the full set of LO contributions and partonic subprocesses, while retaining finite-width effects of the top quarks and the electroweak gauge bosons. Resonant and non-resonant contributions as well as interference effects are included in the complete calculation. We pay special attention to infrared singularities associated with photons and jets appearing simultaneously in the final state. Fiducial integrated and differential cross-section results are presented for $pp$ collisions at $\sqrt{s}=13.6$ TeV.