Analysis of theZ0Resonant Amplitude in GeneralRξGauges

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.