  Top quark production in the process $e^+e^- \to t\bar{t}$ at a future linear
electron positron collider with polarised beams is a powerful tool to determine
indirectly the scale of new physics. The presented study, based on a detailed
simulation 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 pair
decays semi-leptonically and the cross sections and the forward-backward
asymmetries are determined. Based on these results, the vector, axial vector
and tensorial $CP$ conserving couplings are extracted separately for the photon
and the $Z^0$ component. With the expected precision, a large number of models
in which the top quark acts as a messenger to new physics can be distinguished
with many standard deviations. This will dramatically improve expectations from
e.g. the LHC for electro-weak couplings of the top quark.

High Energy Physics - Experiment;High Energy Physics - Phenomenology