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Top quark production in the process $e^+e^- \rightarrow t\bar{t}$ at a futurelinear electron positron collider with polarised beams is a powerful tool todetermine indirectly the scale of new physics. The presented study, based on adetailed simulation of the ILD detector concept, assumes a centre-of-massenergy of $\roots=500$\,GeV and a luminosity of $\mathcal{L}=500\,\invfb$equality shared between the incoming beam polarisations of $P_{e^{-,+}}=\pm0.8,\mp0.3$. Events are selected in which the top pair decayssemi-leptonically. The study comprises the cross sections, the forward-backwardasymmetry and the slope of the helicity angle asymmetry. The vector, axialvector and tensorial CP conserving couplings are separately determined for thephoton and the $Z^0$ component. The sensitivity to new physics would bedramatically improved with respect to what is expected from LHC for electroweakcouplings.

A precise determination of top quark electro-weak couplings at the ILC operating at $\roots=500\,\GeV$