  It has been proposed that the coherent propagation of long-lived heavy neutrino mass eigenstates can lead to an oscillating rate of lepton number conserving (LNC) and violating (LNV) events, as a function of the distance between the production and displaced decay vertices. We discuss this phenomenon, which we refer to as heavy neutrino-antineutrino oscillations, in the framework of quantum field theory (QFT), using the formalism of external wave packets. General formulae for the oscillation probabilities and the number of expected events are derived and the coherence and localisation conditions that have to be satisfied in order for neutrino-antineutrino oscillations to be observable are discussed. The formulae are then applied to a low scale seesaw scenario, which features two nearly mass degenerate heavy neutrinos that can be sufficiently long lived to produce a displaced vertex when their masses are below the $W$ boson mass. The leading and next-to-leading order oscillation formulae for this scenario are derived. For an example parameter point used in previous studies, the kinematics of the considered LNC/LNV processes are simulated, to check that the coherence and localisation conditions are satisfied. Our results show that the phenomenon of heavy neutrino-antineutrino oscillations can indeed occur in low scale seesaw scenarios and that the previously used leading order formulae, derived with a plane wave approach, provide a good approximation for the considered example parameter point. 
Heavy Neutrino-Antineutrino Oscillations in Quantum Field Theory