The fermion-loop scheme for finite-width effects in e+et- annihilation into four fermions

Abstract

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 t- e + → four fermions, with massless external fermions. The fermion-loop scheme consists in including all fertnionic 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 self-energies 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 t-e + → μ t- ν μu d, e t-e + → s cu d , and e t-e + → e t- ν er d , and give numerical comparisons with other gauge-invariance-preserving schemes in the energy range of LEP2, NLC and beyond.