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\label{sec:Higgs}  The primary goal of a Higgs factory is to measure the Higgs boson properties with a precision deemed adequate to be sensitive to Physics beyond the standard model. Tree-level couplings of the Higgs boson to fermions and gauge bosons are expected be modified with respect to the standard-model prediction, with a magnitude rapidly decreasing with the new Physics scale $\Lambda$, typically like $1/\Lambda^2$. For $\Lambda = 1$ TeV, departures up to 5\% are expected~\cite{Gupta_Rzehak_Wells_2012,cite:ILCTDR}. To discover new Physics through its effects on the Higgs boson couplings with a significance of 5$\sigma$, it is therefore necessary to measure these couplings to fermions and gauge bosons with a precision of 1\%, and actually at the per-mil level if the if $\Lambda$ is to be larger than 1 TeV, as hinted at by the negative results of the searches at LHC.   The number of Higgs bosons expected to be produced, hence the integrated luminosity delivered by the collider, are therefore key elements in the choice of the right Higgs factory for the future of high-energy physics: a per-mil accuracy cannot be reached with less than a million Higgs bosons. The Higgs production cross section~\cite{cite:HZHA}, section (obtained with the {\tt HZHA} generator~\cite{cite:HZHA}),  through the Higgs-strahlung process $\epemto {\rm HZ}$ and the ${\rm WW}$ or ${\rm ZZ}$ fusion processes, is displayed in Fig.~\ref{fig:HiggsCross}. A convenient centre-of-mass energy to maximize the number of Higgs boson produced is around 250 GeV, where the total production cross section amounts to 200~fb. The instantaneous luminosity profile of TLEP (Fig.~\ref{fig:lumi}) leads to choose a slightly smaller optimal value, $\sqrt{s} = 240$ GeV.