NLO QCD corrections to off-shell top-antitop production with semi-leptonic decays at lepton colliders

The study of top-quark properties will be a central aspect of the physics programme of any future lepton collider. In this article, we investigate the production of top-quark pairs in the semi-leptonic decay channel in $e^{+}{e}^{-}$ collisions, whose experimental signature is one charged lepton, jets, and missing energy. We present for the first time fiducial cross sections and differential distributions at next-to-leading-order accuracy in QCD for the full off-shell process. We find that the QCD corrections for the considered process are strongly dependent on the beam energies and range from few per cent up to more than 100% (near threshold and above 1 TeV). We focus, in particular, on two scenarios: one close to threshold (365 GeV), dominated by top-pair production, and one at the TeV scale (1.5 TeV), for which irreducible-background contributions become relevant. An assessment of polarised-beam effects is also provided.