Precision Electroweak measurements at the FCC-ee

Because of a luminosity of up to five orders of magnitude larger than at LEP, electroweak precision measurements at the FCC-ee -- the Future Circular Collider with electron-positron beams -- would provide improvements by orders of magnitude over the present status and constitute a broad search for the existence of new, weakly interacting particles up to very high energy scales. The FCC-ee will address centre-of-mass energies ranging from below the Z pole to the $\mathrm{t\bar{t}}$ threshold and above. At energies around the Z pole, the Z-boson mass and width can be measured to better than 100 keV each. Asymmetry measurements at the Z pole allow improvements in the determination of the weak mixing angle by at least a factor 30 to $\delta\sin^2\theta\mathrm{_W^{eff}}\simeq 6\times 10^{-6}$. A determination of the electromagnetic coupling constant at the Z energy scale, $\alpha_\mathrm{QED}(m_\mathrm{Z}^2)$, to a relative precision of $3\times 10^{-5}$ can be obtained via measurement of the forward-backward asymmetry of lepton pairs at two energy points $\pm 3.2\,\textrm{GeV}$ away from the Z peak. At energies around the WW threshold, high-statistic cross section measurements can provide a determination of the W mass to 300 keV. The key breakthrough advantage of the FCC-ee in these achievements, beside the large luminosity, is the possibility of a continous, precise determination of the beam energy by resonant depolarization at the Z peak and at the WW threshold. Precise measurements of the hadronic branching fractions of the Z and W bosons allow for considerably improvements in the determination of the strong coupling constant down to a precision of $\delta\alpha_\mathrm{s}(m_\mathrm{Z}^2)\simeq 0.0001$. An energy scan around the 350 GeV $\mathrm{t\bar{t}}$ threshold allows a 10 MeV measurement of the top-quark mass.