Finite Width Effects and Gauge Invariance in Radiative $W$ Production and Decay

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, $q{\bar{q}}^{\mathrm{\prime }}\to \mathrm{\ell }\nu \gamma$, 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.