deletions | additions       diff --git a/bf_Discussion_The_above_results__.tex b/bf_Discussion_The_above_results__.tex  index 9012720..310fa84 100644  --- a/bf_Discussion_The_above_results__.tex  +++ b/bf_Discussion_The_above_results__.tex 
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The accuracy of the CP-violating form factors with the sole lepton angle and energy distributions is moderately constraining ($1.4\, 10^{-1}$ on $F_{2A}^\gamma$ and $8.2\, 10^{-1}$ on $F_{2A}^Z$) because of the important correlation between the two distributions $f_D^\gamma$ and $f_D^Z$, well visible in Fig.~\ref{fig:distributions}. A relevant precision of $1.7\, 10^{-2}$, however, is reached on the linear combination $F_{2A}^\gamma + 0.17 \times F_{2A}^Z$ with $2.4\,{\rm ab}^{-1}$ at $\sqrt{s} = 365$\,GeV, reduced to $0.9\, 10^{-2}$ with $500\,{\rm fb}^{-1}$ at $\sqrt{s} = 500$\,GeV. A reduction of the correlation between these two form factors requires the analysis of additional observables, beyond the scope of the present study.  Similarly, when all eight parameters are considered simultaneously, the lepton angle and energy distributions are no longer sufficient to avoid large correlations between form factors. The same observation was made in Refs.~\cite{Baer_2013} and~\cite{Amjad_2013} with the four observables chosen for the analysis at 500\,GeV and with incoming beam polarizations. A generator-level exercise with more observables in the fully leptonic final state has been recently attempted in Ref.~\cite{ledib_2015}, released after the present study. In this exercise, an optimal-observable analysis of the matrix element squared is carried out with thirteen different observables (the top quark direction, the $\ell^+$ and $\ell^-$ angles and energies, the ${\rm b}$ and ${\rm \bar b}$ angles and energies, and the invariant masses of the top quarks and W bosons), with unambiguous identification and reconstruction under the assumption of a perfect detector. The With these additional variables, the  few degeneracies between form factors are indeed removed, and but  the conclusion is identical to that of this paper: the incoming beam polarizations are not essential in the process. A similar analysis could be undertaken for semi-leptonic final states at $\sqrt{s} = 365$\,GeV, in order to determine all eight form factors simultaneously with the ultimate accuracy, but the assumption of a perfect detector cannot be expected to give fully reliable results when the jets and the missing energy from the top decays are to be included, as acknowledged in Ref.~\cite{ledib_2015}. Such an analysis will be carried out when a complete simulation and reconstruction in a realistic detector becomes available for the FCC-ee study.