Abstract
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.
Highlights
In parallel to the applications of neutrino oscillations the framework in which they are described has evolved
The results describe the probabilities that the superposition of heavy neutrino mass eigenstates, produced by the decay of a W boson together with an antilepton of flavour α, produces anlepton of flavour β if it decays after a distance L in the direction of p0 via an lepton number conserving (LNC) (LNV) process
In this paper we have applied the framework of quantum field theory (QFT) with external wave packets to derive the probabilities for the oscillations between long-lived heavy neutrino and antineutrino interaction eigenstates, where we define a neutrino as the neutral lepton that is produced together with a charged antilepton and a W boson
Summary
We define neutrinos (antineutrinos) as those particles produced from the decay of a W boson, together with a charged antilepton (lepton), respectively. The results describe the probabilities that the superposition of heavy neutrino mass eigenstates, produced by the decay of a W boson together with an antilepton of flavour α, produces an (anti)lepton of flavour β if it decays after a distance L in the direction of p0 via an LNC (LNV) process.. In order to simplify the expression eq (2.12), following the above discussion, the spin correlation between the production and detection vertices are neglected This allows to absorb the mass splitting independent parts of the interaction amplitudes in eq (2.12) into the normalisation constant. This leads to the following oscillation probability, which is independent of the mean momenta of the decay products of the heavy neutrino, spins and polarisations of the external particles. Note that if one wanted to consider the spin correlation, one has to use eq (2.16) in the definition of eq (2.34)
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