deletions | additions       diff --git a/Beam polarization.tex b/Beam polarization.tex  index ec20218..14db3dd 100644  --- a/Beam polarization.tex  +++ b/Beam polarization.tex 
...
\subsubsection{Motivations}  Transverse beam polarization builds up naturally Polarized beams are useful for several purposes  in a $\epem$  storage ring by the Sokolov-Telnov effect. rings.  Transverse polarization wasmeasured and  used at LEP for beam energy calibrations calibration  with 0.1 MeV intrinsic  precision~\cite{ement_of_the_W_boson_mass_2005}.A transverse polarization in excess of 5-10\% is sufficient for this purpose, and was obtained up to 61 GeV per beam at LEP. It is generally accepted that this upper limit is determined by the energy spread, which becomes commensurate with the fractional part of the spin-tune $\nu_s = E_{beam}[GeV] /0.440665$. Given that the energy spread scales as $\sigma_E \propto E_{beam}^2 / \sqrt{\rho}$ (where $\rho$ is the bending radius), its effect on the achievable polarization should be reduced in TLEP, so that beam polarization sufficient for energy calibration should be readily available up to and above the WW threshold , i.e. 81 GeV per beam. A new machine with a better handle on the orbit should be able to increase this limit: a full 3D spin tracking simulation of the electron machine of the Large Hadron-electron collider (LHeC) project in the 27 km LHC tunnel resulted in a 20\% polarization at beam energy of 65 GeV for typical machine misalignment~\cite{1206.2913}. Polarization wigglers as described for LEP in Ref.~\cite{cite:Blondel-Jowett-LEP606} would be mandatory for TLEP to decrease the polarization time to an operational value at the Z peak, as without them the polarization time would be nearly 150 hours.  This ability to perform energy calibrations is unique to circular machines, and the exquisite precision of the method is  essential for the precision measurements of the Z mass and width, and of the W mass. Longitudinal polarization was used at SLC for the measurement of the left-right asymmetry at the Z pole, $\ALR$, with a 1.5\% relative precision, which in turn allowed a determination of the weak mixing angle with an accuracy similar to that of the best LEP unpolarized measurements. It is therefore of great interest to establish both transverse and longitudinal polarizations with TLEP, and be able to maintain the latter in collisions at the Z pole.