introduction

where m_Z is the Z mass. In this equation, Dr parametrizes the loop corrections which lead to a quadratic dependence of m_W² on the top quark mass and a smaller logarithmic dependence on the Higgs boson mass (M_H). A global fit of electroweak observables measured at the Z resonance together with m_top and putting M_H to 300 GeV/c² yields a W mass of 80.379 ±0.023 GeV/c² [] in the SM.

The comparison of a direct measurement of m_W with this prediction is one of the important goals of LEP enabling a stringent test of the Standard Model to be made. Furthermore, any significant deviation of m_W outside the known limits on M_H would point to new physics. This paper describes the final measurements of m_W and G_W from ALEPH as a contribution to this goal. Earlier results have been published by DELPHI, L3 and OPAL [,,] and final results from the Tevatron Run 1 p[`p] collider experiments using large samples of single W's decaying into electrons and muons [].

The W mass and width are determined from the direct reconstruction of the invariant mass of its decay products in both the WW®q[`q]q[`q] hadronic and WW® lnq[`q] semileptonic channels. Measurements were published previously in 1998 [] using the data collected at a centre-of-mass (CM) energy of 172 GeV, in 1999 [] at a CM energy of 183 GeV and in 2000 [] at 189 GeV. The latter ALEPH publication included a weighted average result obtained from the combination of all these measurements as well as those obtained earlier from the total W pair cross sections at 161 [] and 172 GeV []. At that time, the statistical precision achieved was 61 MeV/c² for the mass with a systematic uncertainty of 47 MeV/c². These publications were based on data collected up to the end of 1998. In the subsequent two years up to the closure of LEP in 2000, much larger samples of data ( ~ 3 times) were collected at CM energies up to 209 GeV.

For this paper, all these data are included in the analysis except for the samples below 183 GeV which have been discarded as statistically insignificant. Corresponding to an integrated luminosity of 683 , the data are fully reprocessed and analysed homogeneously sub-divided into eight samples at average CM energies of 183, 189, 192, 196, 200, 202, 205 and 207 GeV. This sub-division provides a consistent set of selected events for each topology which are the same samples as those used in the analysis of the WW cross section [].

A constrained kinematic fit employing Lagrange multipliers conserving energy and momentum is applied to each selected event in data and generated by Monte Carlo (MC) simulation. As in previous analyses for each channel, the simulated mass spectra are fitted to the data after cuts using a reweighting technique to extract the W mass and width. Very large Monte Carlo productions ( > 10⁶ signal events per CM energy) enable multi-dimensional fits to be used with significant gains in precision. The signal Monte Carlo events are weighted to allow for the effect of O(a) corrections [] in m_W and G_W.

Since the statistical error on m_W is now comparable with the previously published systematic uncertainties, a more detailed evaluation of all important uncertainties is performed. In the more recently reported measurements of m_W at LEP [], the dominant systematic uncertainty in the q[`q]q[`q] channel is due to colour reconnection (CR). Since most models predict that CR affects the topological distribution of lower energy particles, a direct search for any variation in the data is made using alternative jet reconstructions which progressively eliminate these particles. The effect of these reconstructions has been checked using hadronic di-jets from the lnq[`q] channels, where no final state interactions are present, to confirm the absence of any significant mass shifts from other sources. Major improvements have been made to the simulation of neutral particles in the electromagnetic calorimeter. The fine granularity and longitudinal segmentation of the detector elements [] allows closely related energy depositions to be identified. The treatment of these depositions, either within jets or associated with the isolated lepton in m,enq[`q] events, is revised following this more detailed simulation.

The paper is organised as follows. In Section 2, the important properties of the ALEPH detector and event reconstruction for this analysis are recalled as well as new features of the detector simulation. Section 3 contains a full description of the MC event generations for the signal and background processes involved. Section 4 describes the event selection and kinematic reconstruction procedures in the different channels highlighting, where appropriate, the modifications and improvements applied since the earlier analyses at 183 and 189 GeV [,]. Section 5 describes the extraction of m_W and the evaluation of the width G_W. Section 6 describes the specific studies made to set a limit on CR from the data. Section 7 describes all studies of systematic uncertainties. The measurements of m_W and G_W in each channel are combined in Sect. 8, taking into account common sources of systematic uncertainties. The W masses obtained from the purely hadronic q[`q]q[`q] channel and from the combined semileptonic channels are compared in Sect. 9. Final conclusions and their interpretation are discussed in Sect. 10.