Theoretical considerations concerning the Z⁰ mass

We compare two previously introduced theoretical definitions of the Z⁰ mass and show that one of them, frequently used, is gauge dependent in O(α³) in a wide class of gauges and in O(α²) in the complementary class. We then discuss a slightly modified version that circumvents these problems, is endowed with desirable theoretical properties, and can be identified with the mass measured at the CERN e⁺{e}^{{{-}}}$ collider LEP. The simple formulation that emerges is applied to illustrate properties of the physical amplitude, related to gauge invariance, and the role played by the two definitions of mass.