  Now that the mass of the Higgs boson is known, circular electron positron
colliders, able to measure the properties of these particles with high
accuracy, are receiving considerable attention. Design studies have been
launched (i) at CERN with the Future Circular Colliders (FCC), of which an e+e-
collider is a potential first step (FCC-ee, formerly caller TLEP) and (ii) in
China with the Circular Electron Positron Collider (CEPC). Hosted in a tunnel
of at least 50 km (CEPC) or 80-100 km (FCC), both projects can deliver very
high luminosity from the Z peak to HZ threshold (CEPC) and even to the top pair
threshold and above (FCC-ee). At the ZH production optimum, around 240 GeV, the
FCC-ee (CEPC) will be able to deliver 10 (5) ab-1 integrated luminosity in 5
(10) years with 4 (2) interaction points: hence to produce millions of Higgs
bosons through the Higgsstrahlung process and vector boson fusion processes.
This sample opens the possibility of subper- cent precision absolute
measurements of the Higgs boson couplings to fermions and to gauge-bosons, and
of the Higgs boson width. These precision measurements are potentially
sensitive to multi-TeV range new physics interacting with the scalar sector.
The ZH production mechanism also gives access to the invisible or exotic
branching ratios down to the per mil level, and with a more limited precision
to the triple Higgs coupling. For the FCC-ee, the luminosity expected at the
top pair production threshold (sqrt(s) ~ 340-350 GeV) further improves some of
these accuracies significantly, and is sensitive to the Higgs boson coupling to
the top quark.
