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\section{Summary and outlook}
In this paper, it has been shown that the measurements of the angular and energy distributions in semi-leptonic ${\rm t\bar t}$ events (${\rm e^+e^- \to t \bar t} \to \ell \nu {\rm q \bar q b \bar
b}$ b}$) at future ${\rm e^+e^-}$ colliders have a strong potential for a precise determination of the top-quark electroweak couplings.
It has been demonstrated, even with the sole use of these two distributions and modest detector performance, that the lack of incoming beam polarization at the FCC-ee is
more than compensated by the
use polarization of the final state
polarization top quarks, and by a significantly larger integrated
luminosity, even with the sole use of the lepton energy and angular distributions, and modest detector performance. luminosity.
The present study is only a first look at this topic for Although these projections were obtained with somewhat conservative hypotheses on the
FCC-ee. It enhances detector performance, it will also be important to reproduce the
fantastic potential of a 100-km circular ${\rm e^+e^-}$ collider already envisioned in Ref.~\cite{Bicer_2014} results with
the a full
profiling of the top quark from simulation in a
precise measurement of its electroweak couplings. It becomes now of particular interest Monte Carlo study, as to
check further investigate that the
added value of these measurements to detector requirements are indeed quite modest. While the
sensitivity to new physics, when combined inferred precisions are already competitive with
other projects on the
unequalled precision of the measurements market, such a Monte Carlo study will allow a reliable reconstruction of
all observables in the
Z, event, beyond the
W, lepton energies and
directions, and is expected to bring sizeable improvements, especially on the
Higgs boson properties, as well as of the top-quark mass, at the FCC-ee. few remaining correlations between form factors.
Although the The present
projections were obtained with somewhat conservative hypotheses on the detector performance, it will also be important to reproduce these results with study is only a
Monte Carlo study, as to further investigate that first look at this topic for the
detector requirements are indeed quite modest. While FCC-ee. It enhances the
inferred precisions are fantastic potential of a 100-km circular ${\rm e^+e^-}$ collider already
competitive envisioned in Ref.~\cite{Bicer_2014} with
other projects on the
market, this study will benefit from, for example, the energy and angular distrbutions full profiling of the
b-quark jets and top quark from a precise measurement of its electroweak couplings. In view of these new estimates, it becomes of particular interest to check their
correlations with added value to the
lepton distributions, sensitivity to
improve new physics, especially when combined with the
unequalled precision
on all couplings and in particular on $F_{1A}^Z$. Finally, the CP-violating form factors, ignored in this study for of the
sake measurements of
an easy comparison with Ref.~\cite{Baer_2013}, will have to be included too. Event variables, such as the
asymmetry between Z, the
negative W, and the
positive lepton distributions~\cite{Grzadkowski_2000}, will be interesting to study in this perspective. Higgs boson properties, as well as of the top-quark mass, at the FCC-ee.