  We base a new wave-function renormalization prescription on the pole mass
renormalization prescription, in which the Wave-function Renormalization
Constant (WRC) is extracted by expanding the particle's propagator around its
pole, rather than its physical mass point as convention. We find the difference
between the new and the conventional WRC is gauge-parameter dependent for
unstable particles beyond one-loop level, which will lead to some physical
results gauge dependent under the conventional wave-function renormalization
prescription beyond one-loop level.
