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A summary of the statistical precision of the measurements presented in Ref. \cite{cite:1208.1662} for \(\sqrt{s}=240\) GeV – extrapolated to the TLEP luminosity and to four detectors – is given in Table \ref{tab:HiggsBranching}. In this table, a few numbers are added with respect to Ref. \cite{cite:1208.1662}. First, the precision for \(\sigma_{\rm HZ}\times{\rm BR(H\to c\bar{c})}\) and \(\sigma_{\rm HZ}\times{\rm BR(H\to gg)}\) is extrapolated from the ILC prediction, as would be obtained if the CMS detector were upgraded with a vertex detection device with adequate c-tagging performance. Secondly, the precision for \(\sigma_{\rm HZ}\times{\rm BR(H\to ZZ)}\) is obtained from an almost background-free dedicated search for ZZZ final states including four leptons, recently developed for that purpose.

\label{tab:HiggsBranching}Statistical precision for Higgs measurements obtained from the proposed TLEP programme at \(\sqrt{s}=240\) GeV only (shown in Table \ref{tab:HiggsCross}). For illustration, the baseline ILC figures at \(\sqrt{s}=250\) GeV, taken from Ref. —\cite{ILC:Physics}—, are also given. The order-of-magnitude smaller accuracy expected at TLEP in the \({\rm H}\to\gamma\gamma\) channel is the threefold consequence of the larger luminosity, the superior resolution of the CMS electromagnetic calorimeter, and the absence of background from Beamstrahlung photons.
	TLEP 240	ILC 250
\(\sigma_{\rm HZ}\)	0.4%	2.5%
\(\sigma_{\rm HZ}\times{\rm BR(H\to b\bar{b})}\)	0.2%	1.1%
\(\sigma_{\rm HZ}\times{\rm BR(H\to c\bar{c})}\)	1.2%	7.4%
\(\sigma_{\rm HZ}\times{\rm BR(H\to gg)}\)	1.4%	9.1%
\(\sigma_{\rm HZ}\times{\rm BR(H\to WW)}\)	0.9%	6.4%
\(\sigma_{\rm HZ}\times{\rm BR(H}\to\tau\tau{\rm)}\)	0.7%	4.2%
\(\sigma_{\rm HZ}\times{\rm BR(H\to ZZ)}\)	3.1%	19%
\(\sigma_{\rm HZ}\times{\rm BR(H}\to\gamma\gamma{\rm)}\)	3.0%	35%
\(\sigma_{\rm HZ}\times{\rm BR(H}\to\mu\mu{\rm)}\)	13%	100%

The latter measurement has an important consequence for the determination of the total Higgs decay width. In \({\rm e}^{+}{\rm e}^{-}\) collisions, it is not possible to directly observe the width of the Higgs boson if it is as small as the Standard Model prediction of 4 MeV. However, the total width of the Higgs boson is given by \(\Gamma_{\rm tot}=\Gamma{\rm(H\to ZZ)}/{\rm BR(H\to ZZ)}\). The partial decay width \(\Gamma{\rm(H\to ZZ)}\) is directly proportional to the inclusive cross section \(\sigma_{\rm HZ}\), measured with a precision of 0.4% from the “recoil mass” distribution of Fig. \ref{fig:Recoil}. The Higgs boson branching ratio to ZZ, \({\rm BR(H\to ZZ)}\), is in turn obtained from the number of ZZZ events, itself proportional to \(\sigma_{\rm HZ}\times{\rm BR(H\to ZZ)}\), measured with a 3.1% relative precision. Therefore, with the sole 240 GeV data, TLEP is able to determine the Higgs boson decay width with a precision of the order of 3% from this channel. The \({\rm H\to b\bar{b}}\nu\bar{\nu}\) final state produced via WW fusion can also be used for that purpose, as described in more detail in the next section.