Discovering heavy neutrino-antineutrino oscillations at the Z-pole

Collider-testable type I seesaw extensions of the Standard Model are generally protected by an approximate lepton number (LN) symmetry. Consequently, they predict pseudo-Dirac heavy neutral leptons (HNLs) composed of two nearly degenerate Majorana fields. The interference between the two mass eigenstates can induce heavy neutrino-antineutrino oscillations (\( N\overline{N}\textrm{Os} \)) leading to observable lepton number violation (LNV), even though the LN symmetry is approximately conserved. These \( N\overline{N}\textrm{Os} \) could be resolved in long-lived HNL searches at collider experiments, such as the proposed Future Circular e⁺e⁻ Collider (FCC-ee) or Circular Electron Positron Collider (CEPC). However, during their Z-pole runs, the LN carried away by the light (anti)neutrinos produced alongside the HNLs prevents LNV from being observed directly. Nevertheless, \( N\overline{N}\textrm{Os} \) materialise as oscillating signatures in final state distributions. We discuss and compare a selection of such oscillating observables, and perform a Monte Carlo simulation to assess the parameter space in which \( N\overline{N}\textrm{Os} \) could be resolved.