\subsection{Global fit for Higgs boson couplings}
\label{sec:FitResults}

The accuracies on the Higgs boson couplings are obtained here from a fit to all observables reported in Tables~\ref{tab:HiggsBranching} and~\ref{tab:WWFusion} for TLEP at $\sqrt{s}=$ 240 and 350 GeV. The fit closely follows the logic presented in Ref.~\cite{cite:1207.2516}, and indeed reproduces the results presented therein for the combination of the ILC and LHC projections. Here, the results of standalone fits, i.e., without combination with LHC sensitivities, are given so as to compare the LHC, ILC and TLEP relative performance in terms of Higgs boson coupling and width measurements. The other two assumptions made in Ref.~\cite{cite:1207.2516} consist in  {\it (i)} bounding from above the couplings to the Z and the W to the Standard Model couplings; and {\it (ii)} saturating the exotic decay width by the sole invisible Higgs boson decays. These assumptions introduce some model dependency which are not called for when it comes to measure the Higgs boson properties in a truly model-independent manner. These two assumptions were therefore removed from the fit, the results of which are presented in the first three columns of Table~\ref{tab:FitResults} and in Fig.~\ref{fig:FitResults}. For completeness, and for direct comparison with Ref.~\cite{cite:1207.2516}, the results of the fit with these two assumptions are also given in the last two columns of the same table. 

\begin{table}
\begin{center}
\caption{Relative statistical uncertainty on the Higgs boson couplings, as expected from the physics programme at $\sqrt{s} = 240$ and $350$ GeV at TLEP. The numbers between brackets indicates the uncertainties expected with two detectors instead of four. For illustration, the uncertainties expected from the ILC baseline programme at 250 and 350 GeV are also given. The first three columns give the results of a truly model-independent fit, while the last two include the two assumptions made in Ref.~\cite{cite:1207.2516} on the W/Z couplings and on the exotic decays, for completeness and easier comparison. The column labelled "TLEP-240" holds for the sole period at 240 GeV for TLEP. The last line gives the {\it absolute} uncertainty on the Higgs boson branching fraction to exotic particles (invisible or not).\label{tab:FitResults}}
\begin{tabular}{|r|r|rl|r|r|rl|r|}
\hline Coupling & TLEP-240 & TLEP & & ILC  &  & TLEP & & ILC\\ \hline
\hline $g_{\rm HZZ}$  & 0.16\% & {\bf 0.15\%} & (0.18\%) & 0.9\% &  & 0.05\% & (0.06\%) & 0.31\% \\ 
\hline $g_{\rm HWW}$  & 0.85\% & {\bf 0.19\%} & (0.23\%) & 0.5\% &  & 0.09\% & (0.11\%) & 0.25\% \\ 
\hline $g_{\rm Hbb}$  & 0.88\% & {\bf 0.42\%} & (0.52\%) & 2.4\% &  & 0.19\% & (0.23\%) & 0.85\% \\ 
\hline $g_{\rm Hcc}$  & 1.0\% & {\bf 0.71\%}  & (0.87\%) & 3.8\% &  & 0.68\% & (0.84\%) & 3.5\% \\ 
\hline $g_{\rm Hgg}$  & 1.1\% & {\bf 0.80\%}  & (0.98\%) & 4.4\% &  & 0.79\% & (0.97\%) & 4.4\% \\ 
\hline $g_{{\rm H}\tau\tau}$  & 0.94\% & {\bf 0.54\%} & (0.66\%) & 2.9\% &  & 0.49\% & (0.60\%) & 2.6\% \\ 
\hline $g_{{\rm H}\mu\mu}$  & 6.4\% & {\bf 6.2\%} & (7.6\%) & 45\% &  & 6.2\% & (7.6\%) & 45\% \\ 
\hline $g_{{\rm H}\gamma\gamma}$ &1.7\% & {\bf 1.5\%} & (1.8\%) & 14.5\% &  & 1.4\% & (1.7\%) & 14.5\% \\ \hline
\hline ${\rm BR}_{\rm exo}$ & 0.48\% & {\bf 0.45\%} & (0.55\%) & 2.9\% &  & 0.16\% & (0.20\%) & 0.9\% \\ \hline
\end{tabular} 
\end{center}
\end{table}