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Top quark production in the process $e^+e^- \to t\bar{t}$ at a future linearelectron positron collider with polarised beams is a powerful tool to determineindirectly the scale of new physics. The presented study, based on a detailedsimulation of the ILD detector concept, assumes a centre-of-mass energy of$\sqrt{s}=500\,$GeV and a luminosity of $\mathcal{L}=500\,{\rm fb}^{-1}$equally shared between the incoming beam polarisations of $\mathcal{P}_{e^-},\mathcal{P}_{e^+} =\pm0.8,\mp0.3$. Events are selected in which the top pairdecays semi-leptonically and the cross sections and the forward-backwardasymmetries are determined. Based on these results, the vector, axial vectorand tensorial $CP$ conserving couplings are extracted separately for the photonand the $Z^0$ component. With the expected precision, a large number of modelsin which the top quark acts as a messenger to new physics can be distinguishedwith many standard deviations. This will dramatically improve expectations frome.g. the LHC for electro-weak couplings of the top quark.

A precise characterisation of the top quark electro-weak vertices at the ILC