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\section{Introduction}  \label{sec:Introduction}  The design study of the Future Circular Colliders (FCC) in a 100-km ring in the Geneva area has started at CERN at the beginning of 2014, as an option for a post-LHC particle accelerators. The study has an emphasis on proton-proton and electron-positron high-energy frontier machines~\cite{FCCWebSite}. In the current plans, the first step of the FCC physics programme would make use exploit a high-luminosity  ofthe  ${\rm e^+e^-}$ collider, collider  called FCC-ee, with centre-of-mass energies ranging from below the Z pole to the ${\rm t\bar t}$ threshold and beyond. A first look at the physics case of the FCC-ee can be found in Ref.~\cite{Bicer_2014}. In this first look, the focus regarding top-quark physics was on precision measurements of the top-quark mass, width and Yukawa coupling through a scan of the ${\rm t\bar t}$ production threshold, with $\sqrt{s}$ comprised between~340 and~350\,GeV. The expected precision on the top-quark mass is in turn used in a global electroweak fit to set constraints on weakly-coupled new physics up to a scale of 100\,TeV. Although not alluded to in the first look, new physics might also show up via significant deviations of the top-quark electroweak couplings with respect to their standard-model predictions. Theories in which the top quark and the Higgs boson are composite lead to such deviations. The inclusion of a direct measurement of the ttZ coupling in the global electroweak fit is therefore likely to further constrain these theories.