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 mag netic bending field by 16 NMR probes situated in a number of the LEP dipole s. The relationship between the fields measured by the probes and the beam energy is calibrated against precise measurements of the average beam energ y between 41 and 55 GeV made using the resonant depolarisation technique. T he linearity of the relationship: is tested by comparing the fields measure d by the probes with the total bending field measured by a flux loop. This test results in the largest contribution to the systematic uncertainty. Sev eral further corrections are applied to derive 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 thc:data taken in 1997, corresponding to a relative precision of 2.7 x 10(-4). This is small in comparison to the present uncertainty on the W mas s 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.