Absolute beam energy measurements in e+e- storage rings

The CERN Large Electron Positron collider (LEP) has been dedicated to the measurement of the mass Mz and the width Gz of the Z0 resonance during the LEP1 phase terminated in September 1995. The Storage Ring has been operated in Energy Scan mode during the 1993 and 1995 physics runs by choosing the beam energy Ebeam to correspond to a CM energy at the IP's EpeakCM ± 1762 MeV. After a short review of the techniques usually adopted to set and control the beam energy, this paper describes in more detail two methods adopted at LEP for precise beam energy determination, essential to reduce the contribution to the systematic error on Mz and Gz. The positron beam momentum was initially determined at the 20 GeV injection energy by measuring the speed of a less relativistic proton beam circulating on the same orbit, taking advantage from the unique possibility of injecting the two beams into LEP at short time intervals. The positron energy at the Z0 peak was in this case derived by extrapolation. Once transverse polarization became reproducibly available, the Resonant Depolarization (RD) technique was implemented at the Z0 operating energies providing a ¾ 2 ¥ 10-5 instantaneous accuracy. RD Beam Energy Calibration has been adopted during the LEP Energy Scan campaigns as well as in Accelerator Physics runs for accurate measurement of machine parameters.