Displaced Signals from Long-lived Particles in Neutrinoless Double Beta Decay

Much of the literature on neutrinoless double beta ($0\nu \beta \beta$) decay with light new-physics mediators focuses on invisible missing energy. We investigate the scenario in which a massive Majoron-like particle $\phi$ is produced on-shell during $0\nu \beta \beta$ decay and subsequently decays into visible final states after travelling a macroscopic distance. Specifically, we analyze the displaced energy deposition from $\phi$ decays into a photon pair ($\gamma \gamma$), a photon and a dark photon ($\gamma {\gamma }_D$) and an electron-positron pair ($e^{+}{e}^{-}$). We demonstrate that the displaced decays modify the expected visible energy spectra and provide novel, distinct experimental signatures at current and upcoming $0\nu \beta \beta$ experiments, with the promise of improving the sensitivity of the standard invisible Majoron searches in $0\nu \beta \beta$ decay by more than two orders of magnitude. The relevant effective couplings can naturally arise in well-motivated ultraviolet-complete scenarios that conventional $0\nu \beta \beta$ decay searches cannot probe.