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

The incorporation of finite-width effects in the theoretical predictions fo r tree-level processes e(+)e(-) --> n fermions requires that gauge invarian ce 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-ca lled Fermion-Loop scheme. It consists in the re-summation of the fermionic one-loop corrections to the vector-boson propagators and the inclusion of a ll remaining fermionic one-loop corrections, in particular those to the Yan g-Mills vertices, In the original formulation, the Fermion-Loop scheme requ ires that vector bosons couple to conserved currents, i.e. that the masses of all external fermions be neglected, There are several examples where fer mion masses must be kept to obtain a reliable prediction. The most famous o ne 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 colli near, within a small cone, with the incoming electron. Therefore, m(e) cann ot 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(-)n u(e)<(nu)over bar>(e)) there are multi-peripheral ones that require a non-v anishing 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(n u)-terms and including the contributions from the Higgs-Kibble ghosts in th e 't Hooft-Feynman gauge. Running vector boson masses are introduced and th eir relation with the corresponding complex poles are investigated, It is s hown that any J-matrix element takes a very simple form when written in ter ms of these running masses. A special example of Ward identity, the U(1) Wa rd 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.