$Z$ Boson Decay into Light and Darkness

We study the $Z\to \gamma \bar{\gamma }$ process in which the $Z$ boson decays into a photon $\gamma$ and a massless dark photon $\bar{\gamma }$, when the latter couples to standard-model fermions via dipole moments. This is a simple yet nontrivial example of how the Landau-Yang theorem—ruling out the decay of a massive spin-1 particle into two photons—is evaded if the final particles can be distinguished. The striking signature of this process is a resonant monochromatic single photon in the $Z$-boson center of mass together with missing momentum. LEP experimental bounds allow a branching ratio up to about 10${}^{-6}$ for such a decay. In a simplified model of the dark sector, the dark-photon dipole moments arise from one-loop exchange of heavy dark fermions and scalar messengers. The corresponding prediction for the rare $Z\to \gamma \bar \gamma$decaywidthcanbeexploredwiththelargesamplesof$Z$ bosons foreseen at future colliders.