deletions | additions       diff --git a/Sensitivities.tex b/Sensitivities.tex  index 68d34c2..40f5d42 100644  --- a/Sensitivities.tex  +++ b/Sensitivities.tex 
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{\bf Event reconstruction}   The only reconstructed quantities used for the determination of the covariance matrices are the lepton direction and the lepton energy (or momentum). Both quantities can be reconstructed with very high precision, as was the case with the detectors built for the LEP collider. In addition, as can be seen from Fig.~\ref{fig:distributions}, the standard model distribution $S^0$ and the optimal observables $f_i$ are smooth functions of the lepton polar angle and energy, hence do not call for a detector with state-of-the-art resolutions. The numerical evaluation of the integrals in Eqs.~\ref{eq:firstInt} to~\ref{eq:lastInt} are however performed with 50 bins in $x$ and $\cos\theta$. This procedure corresponds to conservatively assuming a lepton energy resolution of 1\,GeV and a lepton angular distribution resolution  of 20\,mrad, figures vastly exceeded by LEP detectors. {\bf Event selection and particle identification} 
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{\bf Detector acceptance}  The polar-angle coverage of a typical detector at ${\rm e^+ e^-}$ colliders is usually assumed to be from 10 to 170 degrees. To be conservative, the leptons are assumed here to be detected only for $ | \cos\theta |< 0.9$, {\it i.e.}, in a range from 26 to 154 degrees. This effect is emulated by evaluating the integrals of Section~\ref{sec:optimal} Eqs.~\ref{eq:firstInt} to~\ref{eq:lastInt}  between $\cos\theta_{\rm min} = -0.9$ and $\cos\theta_{\rm max} = 0.9$. Given the large value of the minimum lepton energy, the integration bounds over $x$ are left untouched. {\bf Background processes}  The major background identified in Ref.~\cite{Amjad_2013} (which  Ref.~\cite{Baer_2013} is based upon) is  the single-top production in association with a W boson and a b quark, through WW$^\ast$ production, as it leads to the same final state as the top-quark pair production. The corresponding cross section~\cite{Boos_2001} increases fast with the centre-of-mass energy, and depends on the incoming beam polarization. At $\sqrt{s} = 500$\,GeV (case studied in Ref.~\cite{Baer_2013}), the single-top production cross section can reach up to 20\% of the top-pair production cross section in the final state with an electron or a positron and in the ${\rm e^-_L e^+_R}$ initial polarization configuration, but this background has yet to be included in the top-quark electroweak coupling study. At $\sqrt{s} = 360$\,GeV and with unpolarized beams, however, the single-top cross section amount to about 0.1\% of the pair production cross section in the same final state, and can therefore be safely ignored wihtout additional uncertainties. {\bf Other experimental uncertainties}  A number of uncertainties are listed in Ref.~\cite{Baer_2013}, Ref.~\cite{Amjad_2013},  such as those affecting the measurement if of  the beam polarization (which enters crucially the cross section measurement); the effects of beamstrahlung; or the unambiguous  top-quark reconstruction (which enters crucially the forward-backward asymmetry measurement). These uncertaintiesdo not  apply neither  toeither  the FCC-ee or FCC-ee, where beamstrahlung effects are negligible and no beam polarization needs to be measured, nor  to the present study. study, as the top-quark direction does not be to be reconstructed.  The uncertainty on the total cross section is at the per-mil level, and the integrated luminosity measurement can be controlled with an accuracy close to a fraction of a per mil. {\bf Integrated luminosity profile}