deletions | additions       diff --git a/Beam polarization.tex b/Beam polarization.tex  index dddf880..7651db3 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, limited this upper limit being determined  by machine imperfections and energy spread[17]. spread [17].  Given that the energy spread scales as $(E_{beam})^2 / \sqrt{\rho}$ (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 misalignments [18]). Polarization wigglers 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 would allow measurements of the Z mass and width with precisions of 0.1 MeV/$c^2$ or better and the W mass with a precision of 1 MeV/$c^2$ or better.   Transverse beam polarization of 40\% in collisions had been 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 $10^{35}/cm^{2} /s$. 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, resulting peak. Assuming that the level of polarization  in collisions that was observed at LEP can be  a measurement [21] of the beam polarization asymmetry with a precision of the order of $10^{-5}$ – or a precision on $\sin^2\theta_W^{eff}$ of the order of $10^{-6}$ – for one year of data taking. 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.