Heavy neutrino-antineutrino oscillations at the FCC-ee

We discuss the impact of heavy neutrino-antineutrino oscillations (NNOs) on heavy neutral lepton (HNL) searches at proposed electron-positron colliders such as the future circular $e^+e^-$ collider (FCC-ee). During the $Z$ pole run, HNLs can be produced alongside a light neutrino or antineutrino that escapes detection and can decay into a charged lepton or antilepton together with an off-shell $W$ boson. In this case, signals of lepton number violation only show up in the final state distributions. We discuss how NNOs, a typical feature of collider-testable low-scale seesaw models where the heavy neutrinos form pseudo-Dirac pairs, modify such final state distributions. For example, the forward-backward asymmetry (FBA) of the reconstructed heavy (anti)neutrinos develops an oscillatory dependence on the HNL lifetime. We show that these oscillations can be resolvable for long-lived HNLs. We also discuss that when the NNOs are not resolvable, they can nevertheless significantly modify the theory predictions for FBAs and observables such as the ratio of the total number of HNL decays into $\ell^-$ over ones into $\ell^+$, in an interval of the angle~$\theta$ between the HNL and the beam axis. Our results show that NNOs should be included in collider simulations of HNLs at the FCCee.