\subsection{Beam energy measurement}

As mentioned in Section~\ref{sec:beampol}, transverse polarization can be naturally established at TLEP at the Z pole and at the WW threshold. A technique unique to $\epem$ rings, called resonant spin depolarization~\cite{on_Blondel_Assmann_Dehning_1992}, can therefore be used to measure the beam energy with high precision. This technique was developed and successfully used during the LEP1 programme, and allowed the average beam energy to be known with a precision of 1 MeV. The intrinsic precision of the method, 0.1 MeV or better, was not fully exploited  at LEP1 because no attempt was made to perform this measurement during collisions. Instead, regular measurements were performed by separating the beams at the end of physics fills, and it was soon realized that the energy actually drifted with time because of, e.g., tides and stray currents from nearby train tracks, so that an extrapolation had to be made to “predict” the beam energy during collisions. This extrapolation is the dominant contributor to the current systematic uncertainty of 2 MeV on the Z mass and width. 

At TLEP, instead, it will be possible to keep a few non-colliding bunches out of the 4400 (Z pole) or 600 (WW threshold) bunches without significant loss of luminosity, and apply regular resonant spin depolarization on those. This technique will allow continuous beam energy measurements, in the exact same conditions as for the colliding bunches, with an accuracy of 100 keV or so for each measurement, hence with an accuracy of 100 keV/$\sqrt{N}$ for $N$ measurements. With the statistics foreseen to be available at the Z pole, a precision better than 0.1 MeV will therefore be at hand for the Z mass and width measurements. Similarly, at the WW threshold, the beam energy uncertainty should translate to a systematic uncertainty smaller than 0.1 MeV on the W mass.

If polarization cannot be established at higher centre-of-mass energies, the beam energy can be determined from the precise knowledge of the Z and W masses and the use of the energy-momentum conservation in kinematic fits of the $\epemto {\rm Z}\gamma$~\cite{cite:0506115}, $\epemto {\rm ZZ}$, and $\epemto {\rm WW}$ processes. These three processes should allow the average beam energy (and its spread) to be determined at $\sqrt{s} = 240$ and $350$ GeV with a precision sufficient for all practical purposes. 
