Pole wave-function renormalization prescription for unstable particles

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.