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\section{Precise Measurements measurements  of the Higgs boson properties} \label{sec:Higgs}  The primary goal of a Higgs factory is to measure the Higgs boson properties with the best possible precision as to be sensitive to Physics beyond the Standard Model at the highest possible scale. Tree-level couplings of the Higgs boson to fermions and gauge bosons are expected to 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,ILC:Physics}. 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 at most 1\%, and actually at the per-mil level to reach sensitivity to $\Lambda$ larger than 1 TeV, as hinted at by the negative results of the searches at the LHC.