Lepton Number Violating Radiative $W$ Decay in Models with R-parity Violation

Models with explicit R-parity violation can induce new rare radiative decay modes of the $W$ boson into single supersymmetric particles which also violate lepton number. We examine the rate and signature for one such decay, $W\rightarrow \tilde l\gamma$, and find that such a mode will be very difficult to observe, due its small branching fraction, even if the lepton number violating coupling in the superpotential is comparable in strength to electromagnetism. This parallels a similar result obtained earlier by Hewett in the case of radiative $Z$ decays.