Gauge Invariance in Boson Production

Abstract

It is shown how to construct exactly gauge-invariant S-matrix elements for processes involving unstable gauge particles such as the $W$ and $Z^0$ bosons. The results are applied to derive a physically meaningful expression for the cross-section $\sigma(e^+e^-\to Z^0Z^0)$ and thereby provide a solution to the long-standing problem of the unstable particle. The problem of maintaining QED gauge-invariance in the process $e^+e^-\to\bar\nu_e e^-W^+\to\bar\nu_e e^-u\bar d$ is examined.