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\end{eqnarray}  The expected sensitivities on the anomalous top-quark couplings can be derived in any of these parameterizations. Although originally derived with the parameterization of Ref.~\cite{Grzadkowski_2000}, the estimates presented in Section~\ref{sec:sensitivities} and~\ref{sec:summary}, however, use the parameterization of Ref.~\cite{Baer_2013}, for an easy comparison. For the same reason, although it is not needed, the same restrictions as in Ref.~\cite{Baer_2013} are applied here: only the six CP conserving form factors are considered (i.e., the two $F_{2A}^X$ are both assumed to vanish), and either the four form factors $F_{1V,A}^X$ are varied simultaneously while the the two $F_{2V}^X$ are fixed to their standard model values, or vice-versa. A careful reading of Ref.~\cite{Baer_2013} (and references therein) shows that also the form factor $F_{1A}^\gamma$ was kept to its standard model value for the extraction of the final sensitivities.   The tree-level angular and energy distributions of the lepton arising from the ${\rm t \bar t}$ semi-leptonic decays are known analytically as a function of the incoming beam polarizations and the centre-of-mass energy~\cite{Grzadkowski_2000}L energy~\cite{Grzadkowski_2000}:  \begin{equation}  {{\rm d}^2\sigma \over {\rm d}x {\rm d}\cos\theta} = {3\pi\beta\alpha^2(s) \over 2s} B_\ell S_\ell(x,\cos\theta),  \end{equation}