Displaced Searches for Axion-Like Particles and Heavy Neutral Leptons at Mu3e

We present strategies for the Mu3e experiment to search for light, weakly coupled particles produced in rare muon decays, focusing on displaced $e^{+}{e}^{-}$ decays within the hollow target. In most scenarios the backgrounds can be fully suppressed with a suitable set of cuts. We furthermore quantify the interplay between displaced and prompt searches at Mu3e and existing constraints, showing how Mu3e has a unique opportunity to probe unexplored parameter space.