Patrick Janot edited Sensitivities.tex  about 9 years ago

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\section{Sensitivity to the top-quark electroweak couplings}  \label{sec:sensitivities}  The covariance matrices given in Section~\ref{sec:optimal} assume a perfect event reconstruction, a event selection and a  particle identification efficiency and purity  of 100\%, a $4\pi$ detector acceptance, and the absence of background processes. While these hypotheses would not be utterly unrealistic at an ${\rm e^+ e^-}$ collider, a more conservative approach is in order to render the present estimates credible and reliable. {\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.  {\bf Particle Event selection and particle  identification} The event selection relies on the presence of two energetic b-quark jets and one energetic isolated lepton in the final state, accompanied by either two light-quark jets or an additional lepton. At $\sqrt{s} = 360$\,GeV, the lepton momentum can take values between 14 and 115\,GeV/$c$, a range in which an identification efficiency of 80\% can be conservatively assumed, with a negligible fake rate. Similarly, the b-quark jet energies can take values between 50 and 90\,GeV, for which b-tagging algorithms are very efficient and pure, especially with two b jets in the final state. A very conservative b-tagging efficiency of 60\% is assumed here. To emulate these efficiencies, all terms of Eq.~\ref{eq:optimal} are multiplied by $0.6 \times 0.8 = 0.48$.  {\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$, i.e., in a range from 25 to 155 degrees. This effect is emulated by evaluating the integrals of Section~\ref{sec:optimal} with $\cos\theta_{\rm min} = -0.9$ 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