On Gauge Invariance of Breit-Wigner Propagators

We present an approach to bosonic ($Z^0, W^{\pm}$) as well as fermionic (top-quark) Breit-Wigner propagators which is consistent with gauge invariance arguments. In particular, for the $Z^0$-boson propagator we extend previous analyses and show that the part proportional to $k_{\mu} k_{\nu}/M^2$ must be modified near the resonance. We derive a mass shift which agrees with results obtained elsewhere by different methods. The modified form of a resonant heavy fermion propagator is also given.