We describe the gauge-invariant treatment of the finite-width effects of W and Z bosons in the fermion-loop scheme and its application to the six-fermion (LEP2) processes e − e + → four fermions, with massless external fermions. The fermion-loop scheme consists in including all fermionic one-loop corrections in tree-level amplitudes and resumming the self-energies. We give explicit results for the unrenormalized fermionic one-loop contributions to the gauge-boson selfenergies and the triple gauge-boson vertices, and perform the renormalization in a gauge-invariant way by introducing complex pole positions and running couplings. A simple effective Born prescription is presented, which allows for a relatively straightforward implementation of the fermion-loop scheme in LEP1 and LEP2 processes. We apply this prescription to typical LEP2 processes, i.e., e − e + → µ −ν µ ud, e − e + → scud, and e − e + → e −ν e ud, and give numerical comparisons with other gauge-invariance-preserving schemes in the energy range of LEP2, NLC and beyond.

The atomic parity-violation (APV) parameter Q W for a nucleus with n neutrons and z protons has been included in the list of pseudo-observables accessible with the codes TOPAZ0 and ZFITTER. In this way one can add the APV results in the LEP EWWG 'global' electroweak fits, checking the corresponding effect when added to the existing precision measurements. †

A critical assessment is given of the theoretical uncertainty in the predicted cross-sections for large-angle Bhabha scattering at LEP 1, with or without t-channel subtraction. To this end a detailed comparison is presented of the results obtained with the programs ALIBABA and TOPAZ0. Differences in the implementation of the radiative corrections and the effect of missing higher-order terms are critically discussed. § Research supported by a fellowship of the Royal Dutch Academy of Arts and Sciences.

The single-W production mechanism is synonymous to the e + e − annihilation into eν e and a W boson with the outgoing electron lost in a small cone around the beam direction. It requires a Renormalization Scheme that preserves gauge invariance and fermion masses cannot be neglected in the calculation. A recently proposed generalization of the so-called Fermion-Loop scheme is applied to the evaluation of observables at LEP 2 energies. The total contribution to single-W processes can be split, in a gauge invariant manner, into a s-channel component and a t-channel one. The latter is dominated by a regime of low momentum transfer of the outgoing electron and any high-energy Renormalization Scheme, as the G F -one, fails to give the correct description of the scale. The Fermion-Loop scheme automatically converts, among other things, all couplings of the theory into couplings that are running at the appropriate scale. Therefore, in addition to represent the only scheme fully justified on a field-theoretical basis, the Fermion-Loop is the best starting point to include radiative corrections into single-W production. Numerical results are presented, showing a decrease in the predictions that can be sizeable. There is no naive and overall rescaling of α QED in any pragmatic scheme, as the Fixed-Width one, that can reproduce the Fermion-Loop results, at the requested accuracy, for all configurations and for all kinematical cuts.