deletions | additions       diff --git a/Beam polarization.tex b/Beam polarization.tex  index afe5470..d2aabc9 100644  --- a/Beam polarization.tex  +++ b/Beam polarization.tex 
...
Transverse beam polarization builds up naturally in a storage ring by the Sokolov-Telnov effect. Transverse polarization was measured and used at LEP for beam energy calibrations with 0.1 MeV 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, this upper limit being determined by machine imperfections and energy spread, which becomes commensurate with 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 essential for the precision measurements of the Z mass and width, and of the W mass.   Measurements with longitudinal polarization of the $\epem$ system require maintaining beam polarization in collisions. Transverse beam polarization of 40\% in collisions was observed at LEP at Z pole energies (45 GeV per beam) with one collision point, a beam-beam tune shift of 0.04, and a single bunch luminosity of $10^{30}/cm^{2} /s$ ~\cite{cite:LEP-beam-beam-pol}. This would translate for TLEP, taking into account of the smaller value of $\beta_y^{*}$ and the larger number of bunches, in a luminosity of around $10^{35}/cm^{2} /s $ for the same total storage ring beam-beam tune shift. In addition to the polarization wigglers, movable spin rotators as designed for HERA~\cite{cite:HERA-beams} would allow a program of longitudinal polarized beams at the Z peak. The spin rotator design foreseen for LEP requires tilting the experiments and is unpractical for TLEP. Assuming the same level of polarization in collisions at TLEP than what was observed at LEP, and that a fraction of the bunches can be selectively depolarized to ensure longitudinal polarization of the $\epem$ system, a simultaneous measurement~\cite{Blondel:1987wr} of the beam polarization and of the left-right asymmetry $A_{LR}$ can be envisaged. For one year of data taking a precision on $A_{LR}$ of the order of $10^{-5}$ – or a precision on $\sin^2\theta_W^{eff}$ of the order of $10^{-6}$ would be achieved. Other beam polarization asymmetries for selected final states, $A_{FB}^{pol,f}$, will allow precise measurements of the electroweak couplings as well as being an interesting tool for flavour selection.   Obtaining longitudinal polarization at higher energies requires a cancellation of depolarization effects by reducing the spin-tune spread associated with the energy spread. Siberian snake solutions \cite{cite:Wienans-TLEP4} invoking combinations of spin rotators situated around the experiments and polarization wigglers are being discussed. They take advantage of the fact that the TLEP arcs have very low fields and can be overruled by polarization wigglers suitably disposed around the ring. These schemes will need to be worked out and simulated before the feasibility of longitudinal polarization in high energy collisions can be asserted.