deletions | additions       diff --git a/Beam polarization.tex b/Beam polarization.tex  index c27b5a3..6832a5f 100644  --- a/Beam polarization.tex  +++ b/Beam polarization.tex 
...
\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 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, beam at LEP. It is generally accepted that  this upper limit being is  determined by machine imperfections and 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 essential for the precision measurements of the Z mass and width, and of the W mass.