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 $\sigma (e^{+}{e}^{-}\to Z^0{Z}^0)$ 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.

8 pages LaTeX. Uses axodraw.sty and procsla.sty. Talk presented at The Higgs Puzzle --- What can we learn from LEP II, LHC, NLC and FNC, Ringberg Castle, Tegernsee, Germany, 9--13 December, 1996