  Fundamental properties of unstable particles, including mass, width, and
partial widths, are examined on the basis of the Nielsen identities (NI) that
describe the gauge dependence of Green functions. In particular, we prove that
the pole residues and associated definitions of branching ratios and partial
widths are gauge independent to all orders. A simpler, previously discussed
definition of branching ratios and partial widths is found to be gauge
independent through next-to-next-to-leading order. It is then explained how it
may be modified in order to extend the gauge independence to all orders. We
also show that the physical scattering amplitude is the most general
combination of self-energy, vertex, and box contributions that is gauge
independent for arbitrary s, discuss the analytical properties of the NI
functions, and exhibit explicitly their one-loop expressions in the Z-gamma
sector of the Standard Model.
