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This document provides a writeup of all contributions to the workshop on High precision measurements of $alpha_s$: From LHC to FCC-ee held at CERN, Oct. 12--13, 2015. The workshop explored in depth the latest developments on the determination of the QCD coupling $alpha_s$ from 15 methods where high precision measurements are (or will be) available. Those include low-energy observables: (i) lattice QCD, (ii) pion decay factor, (iii) quarkonia and (iv) $tau$ decays, (v) soft parton-to-hadron fragmentation functions, as well as high-energy observables: (vi) global fits of parton distribution functions, (vii) hard parton-to-hadron fragmentation functions, (viii) jets in $e^pm$p DIS and $gamma$-p photoproduction, (ix) photon structure function in $gamma$-$gamma$, (x) event shapes and (xi) jet cross sections in $e^+e^-$ collisions, (xii) W boson and (xiii) Z boson decays, and (xiv) jets and (xv) top-quark cross sections in proton-(anti)proton collisions. The current status of the theoretical and experimental uncertainties associated to each extraction method, the improvements expected from LHC data in the coming years, and future perspectives achievable in $e^+e^-$ collisions at the Future Circular Collider (FCC-ee) with $cal{O}$(1--100 ab$^{-1}$) integrated luminosities yielding 10$^{12}$ Z bosons and jets, and 10$^{8}$ W bosons and $tau$ leptons, are thoroughly reviewed. The current uncertainty of the (preliminary) 2015 strong coupling world-average value, $alpha_s(m_Z)$ = 0.1177 $pm$ 0.0013, is about 1%. Some participants believed this may be reduced by a factor of three in the near future by including novel high-precision observables, although this opinion was not universally shared. At the FCC-ee facility, a factor of ten reduction in the $alpha_s$ uncertainty should be possible, mostly thanks to the huge Z and W data samples available.
This document collects the proceedings of the Parton Radiation and Fragmentation from LHC to FCC-ee workshop (http://indico.cern.ch/e/ee_jets16) held at CERN in Nov. 2016. The writeup reviews the latest theoretical and experimental developments on pa
The prospects for electroweak precision measurements at the Future Circular Collider with electron-positron beams (FCC-ee) are discussed. The Z mass and width, as well as the value of the electroweak mixing angle, can be measured with very high preci
Due to the high anticipated experimental precision at the Future Circular Collider FCC-ee (or other proposed $e^+e^-$ colliders, such as ILC, CLIC, or CEPC) for electroweak and Higgs-boson precision measurements, theoretical uncertainties may have, i
The Future Circular Collider (FCC) at CERN, a proposed 100-km circular facility with several colliders in succession, culminates with a 100 TeV proton-proton collider. It offers a vast new domain of exploration in particle physics, with orders of mag
This document answers in simple terms many FAQs about FCC-ee, including comparisons with other colliders. It complements the FCC-ee CDR and the FCC Physics CDR by addressing many questions from non-experts and clarifying issues raised during the Euro