Analysis of the Z⁰ Resonant Amplitude in General R_xi Gauges

The Z^0 resonant amplitude is discussed in general R_\xi gauges. When the original on-shell definition of the Z^0 mass M is employed, a gauge dependence of M emerges in the next-to-leading approximation which, although small, is of the same magnitude as the current experimental error. In the following order of expansion, these unphysical effects are unbounded. The gauge dependence of M disappears when modified, previously proposed definitions of mass or self-energies, are used. The relevance of these considerations to the concept of the mass of unstable particles is pointed out.