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\end{equation}  which easily relates to the previous parameterization with  \begin{equation}  A_v+\delta A_v = - 2\sin\theta_W \left( F_{1V}^X + F_{2V}^X \right), \ \ B_v+\delta B_v = - 2\sin\theta_W F_{1A}^X, \ \ \\  \delta C_v = 2\sin\theta_W F_{2V}^X { and } \delta D_v = 2i\sin\theta_W F_{2A}^X. \end{equation}  The expected sensitivities 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   \begin{equation}  {{\rm d}^2\sigma \over {\rm d}x {\rm d}\cos\theta} = {3\pi\beta\alpha_{\rm QED}^2 {3\pi\beta\alpha^2(s)  \over 2s} B_\ell S_\ell(x,\cos\theta), \end{equation}  where $\beta$ is the top velocity, $s$ is the centre-of-mass energy squared, $\alpha(s)$ is the running QED coupling constant,  and $B_\ell$ is the fraction of ${\rm t\bar t}$ events with at least one top quark decaying leptonically (about 44\%). As the non-standard form factors $\delta(A,B,C,D)_v$ are supposedly small, only the terms linear in $\delta(A,B,C,D)_v \equiv \delta_i$ are kept: \begin{equation}  S(x,\theta) = S^0(x,\theta) + \sum_{i=1}^8 \delta_i f_i(x,\cos\theta),  \end{equation}