Measurement of the W mass in $e^+ e^-$ annihilation

A measurement of the W mass in the fully hadronic decay channel from the data sample collected by ALEPH during 1996 at centre-of-mass energies of 161 and 172 GeV is presented. At 161 GeV, the W mass is derived from the cross-section measurement taking advantage of the high sensitivity close to the production threshold. Due to the presence of large backgrounds, a multidimensional analysis based on Neural Network techniques is developed. By combining the measurements in all decay channels and the four LEP experiments, a precision in the W mass of $\pm 220$ MeV is finally obtained. At 172 GeV, the W mass is obtained from the direct reconstruction of the final state kinematics. The fully hadronic decay channel becomes particularly difficult due to the large existing background and the important distortions due to fragmentation and detector effects when reconstructing four hadronic jets in the final state. In addition, in this channel there is the intrinsic difficulty associated with the combinatorial background. A sophisticated fitting technique making use of Neural Networks for building up multidimensional probability density functions, as well as an optimal treatment of combinatorial background, has been developed, allowing the determination of the W mass with high accuracy. The LEP combination of the measurements in all decay channels at 172 GeV leads to a precision of about $\pm 170$ MeV. For the sake of completeness, the measurement performed with higher statistics at 183 GeV has been included. By combining all LEP measurements, a W mass determination in good agreement and competitive with the previous measurement at hadron collider experiments is obtained. Finally, from their combination a new world average value is obtained, with an accuracy in the W mass of 64 MeV. The measured W mass is found to be in very good agreement with the indirect measurement from global electroweak fits. Although the measured value seems to prefer a light SM Higgs boson it does not place a strong constraint in its allowed range of values. This situation will change with the increasing statistics to be collected during 1998 and in forthcoming years, when it is expected that a final accuracy in the W mass at the level of 30-40 MeV would be obtained.