Gauge Invariance and Unstable Particles

Abstract

A gauge-independent approach to resonant transition amplitudes with nonconserved external currents is presented, which is implemented by the pinch technique. The analytic expressions derived with this method are $U(1)_{em}$ invariant, independent of the choice of the gauge-fixing parameter, and satisfy a number of required theoretical properties, including unitarity. Although special attention is paid to resonant scatterings involving the $γWW$ and $ZWW$ vertices in the minimal Standard Model, our approach can be extended to the top quark or other unstable particles appearing in renormalizable models of new physics.