Accurate determination of the LEP beam energy by resonant depolarization

The energy calibration of LEP in the 1993 scan

“…Moreover, since depolarization can also occur on synchrotron oscillation satellites of the spin tune, the stability of the tune measurement against a change of the synchrotron tune has to be veri ed. The total systematic error on a single beam energy measurement b y resonant depolarization is about 200 keV as shown by dedicated experimental and theoretical studies [2]. This result is supported by the excellent reproducibility and short-term stability of the measured energy.…”

“…One special calibration was performed in 1993, and two in 1994, to measure the electron and positron beam energies as close to simultaneously as possible. The 1993 calibration indicated an energy di erence larger than 0.5 MeV [2]. The two 1994 calibrations found that the positron beam was 0:0 0:2 MeV and 0:4 0:4 MeV higher in energy than the electron beam.…”

“…To determine the average beam energy uniquely, t w o additional measurements are required to remove a m biguities inherent in the method [2]. A single depolarization cannot determine whether the spin tune is below o r a b o v e the half integer: this ambiguity i s solved by increasing the beam energy with an RF-frequency change and by measuring the direction of the change in the measured spin tune.…”

“…Orbit distortions have t o b e i n troduced to compensate for the spin e ects of the solenoids and to steer the beam into collision with the laser photons from the polarimeter. The individual studies of these di erences are described in section 1 and in reference [2]. In most cases the only signi cant contribution to the systematic errors of the mean energy values arise from the errors common to all calibrations, since repetition reduces the e ects of any random uctuations of the measurements, such as those due to the nite bin size.…”

“…This followed an initial period during which the method of beam energy calibration using resonant depolarization [1] w as commissioned [2]. This paper describes how the centre of mass energies of the colliding beams at the four interaction points were measured during this scan, allowing a more precise determination of the Z mass and width.…”