How effective is the weak mixing angle?

Abstract

The usefulness of an effective weak mixing angle to parameterise the electroweak couplings of quarks and leptons measured at LEP is discussed. After a review of the theoretical formalism used to handle the electroweak radiative corrections to LEP processes, some suggestions for procedures to be used to extract the mixing angle are given and the various definitions of the effective weak mixing angle used by the experiments are examined. This is followed by an attempt to extract a coherent set of mixing angle values from the four experiments with the published 1989/90 (and some 1991) measurements of the Z0 line-shapes, asymmetries and τ polarisation. These results are updated with preliminary results from the 1991 data presented at the XXVI International Conference on High Energy Physics, in Dallas, USA, in August 1992, including the preliminary measurement ofA LR at the SLC. The average value found for the effective weak mixing angle, defined for leptons, is sin2 θ eff lept =02322±0.0010. The error on sin2 θ eff lept can be further reduced by imposing the constraints between the parameters implicit in the MSM. With the additional constraint αs=0.123±0.006 imposed in the fit, the result is sin2 θ eff lept , where the central value is form H =300 GeV, and the second error is the variation ifm H is changed to 50 GeV (lower error) and 1000 GeV (upper error). Within the MSM, sin2 θ lept eff is directly related to the top-quark mass, and the corresponding value ism t =153 −25−23 +22+19 GeV, where the errors have the same meaning as those for sin2 θ eff lept . Finally, the prospects for improved precision are discussed.