deletions | additions       diff --git a/Beam polarization.tex b/Beam polarization.tex  index a0a36cd..da210e4 100644  --- a/Beam polarization.tex  +++ b/Beam polarization.tex 
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\subsection{Beam polarization}  Transverse beam polarization builds up naturally in a storage ring by the Sokolov-Telnov effect. Transverse polarization was measured and used at LEP for energy calibrations up to 61 GeV per beam, this upper limit being determined by machine imperfections and energy spread [17]. [17], which becomes commensurate with the spin-tune $\nu_s = .  Given that the energy spread scales as $(E_{beam})^2 $\sigma_E \propto (E_{beam})^2  / \sqrt{\rho}$ (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 therefore be readily available at TLEP up to 81 GeV, i.e. the WW threshold. 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 [18]). Polarization wigglers as described for LEP in~\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 feature is essential for the unique precision achievable at TLEP for the measurements of the Z mass and width and of the W mass. Transverse beam polarization of 40\% in collisions was observed at LEP with one collision point with a beam-beam tune shift of 0.04, yielding a single bunch luminosity of $10^{30}/cm^{2} /s$ [19]. 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 [20] 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 [21] 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 $10^{-6}$ can would  be envisaged. achieved.  Other beam polarization asymmetries for selected final states $A_{FB}^{pol,f}$ will allow precise measurements of the electroweak couplings or flavour selection. Obtaining longitudinal polarization at higher energies requires a cancellation of depolaization effects by reducing the spin-tune spread associated with the energy spread.   A unique feature of circular machines is the accuracy with which the beam energy can be determined. This is due to the availability of the resonant spin depolarization technique which can reach an instantaneous precision of better than 100 keV on the beam energy. We envisage running with extra dedicated non-colliding bunches where polarization can build up and the energy measured continuously with the resonant depolarization technique [16], further improving the above precision.  {\bf  note: references need to be sorted out. }