The naive implementation of finite width effects in processes involving unstable particles can violate gauge invariance. For the example of radiative $W$ production and decay, $q{\overline{q}}^{\prime }\to \ell \nu \gamma$, at tree level, it is demonstrated how gauge invariance is restored by including the imaginary part of triangle graphs in addition to resumming the imaginary contributions to the $W$ vacuum polarization. Monte Carlo results are presented for the Fermilab Tevatron.

• Received 15 March 1995

DOI:https://doi.org/10.1103/PhysRevLett.75.1002