\subsection{Measurements with OkuW}

With more than $2\times 10^8$ W pairs produced at centre-of-mass energies at the WW threshold and above (hence the ``OkuW'' appelation), of which $2.5\times 10^7$ W pairs at $\sqrt{s} \sim 161$~GeV, TLEP will be a W factory as well. Because the quantity of data expected at the WW production threshold is $10^5$ times larger than that produced at LEP, the measurements to be performed by TLEP at this centre-of-mass energy need to be thoroughly reviewed by the starting design study. Here, only brief accounts of the W mass measurement and the determination of the number of active neutrinos are given. A precise measurement of the strong coupling constant can also be done when the large WW event samples expected at $\sqrt{s}=240$ and $350$~GeV are exploited too. 

\subsubsection{The W mass}

The safest and most sensitive measurement of the W mass can be performed at threshold. At LEP~\cite{1302.3415}, this measurement was done at a unique centre-of-mass energy of 161.3~GeV. A more thorough scan, including a point below threshold for calibration of possible backgrounds, should probably be envisioned to provide the redundancy necessary for a precise measurement at TLEP. The measurement is essentially statistics dominated and the only relevant uncertainties are those associated with the definition of the centre-of-mass energy, as described in Section~\ref{sec:exp}. The precision achieved at LEP on $m_{\rm W}$ was about 300~MeV per experiment. A statistical error of 1~MeV on the W mass should therefore be achievable at TLEP per experiment (i.e., 0.5~MeV from a combination of four experiments).  

As energy calibration with resonant depolarization will be available at TLEP at least up to 81~GeV per beam, the threshold scan should involve beam energies close to the point of maximum $m_{\rm W}$ sensitivity and situated at the half-integer spin tune, $\nu_s = 182.5$ and $183.5$, i.e.,  $E_{\rm beam}= 80.4$ and $80.85$~GeV. Because the beam-energy spread and the beamstrahlung are negligibly small at TLEP, this measurement is not sensitive to the delicate understanding of these two effects. A more careful analysis may reveal systematic uncertainties that are relevant at this  level of precision. They should, however, be somewhat similar to those involved in the Z mass measurement from the resonance line shape, i.e., dominated by the uncertainties on the initial state QED corrections and the theoretical parameterization of the WW threshold cross section.  With the same logic as above, these uncertainties should be reducible to a level below 100~keV on $m_{\rm W}$.\\
\textbf{\textit{An overall, statistics-dominated, uncertainty of 500~keV is therefore considered as a reasonable target for the W mass precision at TLEP.}}

