Evaluation of the LEP Centre-of-Mass Energy Above the W-Pair Production Threshold

Knowledge of the centre-of-mass energy at LEP2 is of primary importance to set the absolute energy scale for the measurement of the W-boson mass. The beam energy above 80 GeV is derived from continuous measurements of the magnetic bending field by 16 NMR probes situated in a number of the LEP dipoles. The relationship between the fields measured by the probes and the beam energy is calibrated against precise measurements of the average beam energy between 41 and 55 GeV made using the resonant depolarisation technique. The linearity of the relationship is tested by comparing the fields measured by the probes with the total bending field measured by a flux loop. This test results in the largest contribution to the systematic uncertainty. Several further corrections are applied to derive the the centre-of-mass energies at each interaction point. In addition the centre-of-mass energy spread is evaluated. The beam energy has been determined with a precision of 25 MeV for the data taken in 1997, corresponding to a relative precision of 2.7x10^{-4}. This is small in comparison to the present uncertainty on the W mass measurement at LEP. However, the ultimate statistical precision on the W mass with the full LEP2 data sample should be around 25 MeV, and a smaller uncertainty on the beam energy is desirable. Prospects for improvements are outlined.Comment: 24 pages, 10 figures, Latex, epsfig; replaced by version accepted by European Physical Journal