deletions | additions       diff --git a/Observations.tex b/Observations.tex  index 4eb6e7b..8209c5b 100644  --- a/Observations.tex  +++ b/Observations.tex 
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The first striking observation is that an increase of the centre-of-mass energy far beyond the top-pair production threshold is not particularly relevant to improve the precision on the top-quark electroweak couplings, as already pointed out in Ref.~\cite{Vos_2015}. For four out of five couplings,nearly  optimum precision is actually reached for $\sqrt{s} \simeq 360$\,GeV, 365$\,GeV,  and for the fifth one the precision is within 50\% of optimum at this energy. The expected precision then degrades by up to a factor four with 500\,${\rm fb}^{-1}$ at $\sqrt{s} = 500$\,GeV. It can also be noted that a very decent precision is alredy reached for $\sqrt{s} = 350$\,GeV. The second observation is that the precision reached for these four couplings is at the level of the per mil, and that the tt$\gamma$ and the ttZ couplings can be determined independently with this precision without the need of initial polarization. It is only for $F_{1A}^Z$ that a moderate increase of the centre-of-mass energy would improve the precision by a factor of two, from 2\% 2.2\%  at $\sqrt{s} = 360$\,GeV 365$\,GeV  to 1\% at $\sqrt{s} = 420$\,GeV, 440$\,GeV,  an energy at which the single-top production would need to be included as a background to the study. There are, however, many other observables to be studied in a ${\rm t\bar t}$ event, beyond the energies and angles of the leptons. It was noticed, for example, that a factor of two improvement could be obtained for $\sigma(F_{1A}^Z)$ at $\sqrt{s} = 360$\,GeV by including 365$\,GeV with  the energy and angular distributions of the b quarks in instead of  the covariance matrix. leptons.  The use of the b jets will be the subject of further studies with more detailed event reconstruction algorithms.