MASS AND WIDTH OF UNSTABLE GAUGE BOSONS

It has been proposed that the mass of the Z0 boson should be defined as the real part, and the width of the Z0 as the imaginary part of the complex pole M(c), for the reason that M(c) is gauge invariant (g.i.). Clearly, this definition is only useful if we can calculate the S-matrix up to some accuracy in a g.i. way. This is not at all obvious, since the use of the Z0 dressed propagator mixes up the order of the diagrams, and thus order by order gauge invariance of the S-matrix, in this formulation, becomes an ill-defined concept. By means of an infinitesimal change of the gauge breaking term, we investigate what happens to perturbative gauge invariance of the S-matrix in the non-perturbative energy region of the Z0 resonance. Within the language of perturbation theory, we find that in fact there exists a Ward identity valid in the complex plane, i.e. for complex values of the momenta of the external legs, from which we can derive the gauge invariance of M(c).