deletions | additions       diff --git a/Measurements at the WW threshold.tex b/Measurements at the WW threshold.tex  index 7ac3e98..a4f383f 100644  --- a/Measurements at the WW threshold.tex  +++ b/Measurements at the WW threshold.tex 
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\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 $\pm 300$ MeV/$c^2$ per experiment. A statistical error of 1 MeV/$c^2$ on the W mass should therefore be achievable at TLEP per experiment  (i.e., 0.5 MeV/$c^2$ for from a combination of  the 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/$c^2$ on $m_{\rm W}$.   \\