Unstable particles and non-conserved currents: a generalization of the Fermion-Loop scheme

The incorporation of finite-width effects in the theoretical predictions for tree-level processes e(+)e(-) --> n fermions requires that gauge invariance must not: be violated. Among various schemes proposed in the literature, the most satisfactory, from the point of view of field theory is the so-called Fermion-Loop scheme. It consists in the re-summation of the fermionic one-loop corrections to the vector-boson propagators and the inclusion of all remaining fermionic one-loop corrections, in particular those to the Yang-Mills vertices, In the original formulation, the Fermion-Loop scheme requires that vector bosons couple to conserved currents, i.e. that the masses of all external fermions be neglected, There are several examples where fermion masses must be kept to obtain a reliable prediction. The most famous one is the so-called single-W production mechanism, the process e(+)e --> e(-)<(nu)over bar>(e)f(1)(f) over bar(2) where the outgoing electron is collinear, within a small cone, with the incoming electron. Therefore, m(e) cannot be neglected. Furthermore, among the 20 Feynman diagrams that contribute (for e<(nu)over bar>(e)u (d) over bar final states, up to 56 for e(+)e(-)nu(e)<(nu)over bar>(e)) there are multi-peripheral ones that require a non-vanishing mass also for the other fermions. A generalization of the Fermion-Loop scheme is introduced to account for external, non-conserved, currents. Dyson re-summed transitions are introduced without neglecting the p(mu)p(nu)-terms and including the contributions from the Higgs-Kibble ghosts in the 't Hooft-Feynman gauge. Running vector boson masses are introduced and their relation with the corresponding complex poles are investigated, It is shown that any J-matrix element takes a very simple form when written in terms of these running masses. A special example of Ward identity, the U(1) Ward identity for single-W, is derived in a situation where all currents are non-conserved and where the top quark mass is not neglected inside loops. (C) 2000 Elsevier Science B.V. All rights reserved.