  The decay $K_L \to \gamma \nu \bar{\nu}$ is analyzed within the standard
model. Short-distance contributions are found to dominate, yielding a branching
ratio of $\sim 0.7 \times 10^{-11}$. We examine the possibility that
non-standard model effects might be observed at higher rates. As an example, we
calculate the branching ratio for the process mediated by neutral horizontal
gauge bosons. Notwithstanding some model uncertainties, experimental limits for
lepton number violation constrains these contributions to $\lesssim 2\times
10^{-11}$.
