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arXiv:2602.02804

Wave packet description of Majorana neutrino oscillations in a magnetic field

Artem Popov, Alexander Studenikin, Alexander Tcvirov

hep-phhep-thquant-phSubmitted Feb 2, 2026• Announced Feb 4, 2026
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Abstract

Majorana neutrino oscillations in a magnetic field are considered using the wave packets formalism. The modified Dirac equation for Majorana neutrinos with non-zero transition magnetic moments propagating in a magnetic field is solved analytically in the two flavour case. The expressions for the oscillations probabilities are derived accounting for the decoherence effect emerging at distances exceeding the coherence length. It is shown that for Majorana neutrinos propagating in a magnetic field the coherence length coincides with the coherence length for neutrino oscillations in vacuum when the vacuum frequency is much greater than the magnetic frequency ($ω_{vac} \gg ω_B$), while it is proportional to the cube of the average neutrino momentum if ($ω_{vac} \ll ω_B$). We show that the decoherence effect may appear during neutrino propagation in a magnetic field of supernova.

Comments
22nd Lomonosov Conference proceedings

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Majorana neutrino oscillations in a magnetic field are considered using the wave packets formalism. The modified Dirac equation for Majorana neutrinos with non-zero transition magnetic moments propagating in a magnetic field is solved analytically in the two flavour case. The expressions for the oscillations probabilities are derived accounting for the decoherence effect emerging at distances exceeding the coherence length. It is shown that for Majorana neutrinos propagating in a magnetic field the coherence length coincides with the coherence length for neutrino oscillations in vacuum when the vacuum frequency is much greater than the magnetic frequency (ωvac≫ωBω_{vac} \gg ω_Bωvac​≫ωB​), while it is proportional to the cube of the average neutrino momentum if (ωvac≪ωBω_{vac} \ll ω_Bωvac​≪ωB​). We show that the decoherence effect may appear during neutrino propagation in a magnetic field of supernova.
There is renewed attention to whether we can observe the decoherence effect in neutrino oscillation due to the separation of wave packets with different masses in near-future experiments. As a contribution to this endeavor, we extend the existing formulation based on a single 1D Gaussian wave function to an amplitude between two distinct 3D Gaussian wave packets, corresponding to the neutrinos being produced and detected, with different central momenta and spacetime positions and with different widths. We find that the spatial widths-squared for the production and detection appear additively in the (de)coherence length and in the localization factor for governing the propagation of the wave packet, whereas they appear as the reduced one (inverse of the sum of inverse) in the momentum conservation factor. The overall probability is governed by the ratio of the reduced to the sum.
Abstract Neutrino oscillations in a constant magnetic field are considered. The backward influence of neutrinos on the environment is accounted for using the density matrix formalism. The entanglement of neutrinos with the magnetic field can destroy quantum coherent superposition of different neutrino states and thus lead to the suppression of neutrino oscillations. The master equation for the neutrino density matrix accounting for the effects of quantum decoherence due to entanglement with the magnetic field is derived.
Abstract Recently, several studies of neutrino oscillations in the vacuum have not found the decoherence long expected from the separation of wave packets of neutrinos in different mass eigenstates. We show that such decoherence will, on the other hand, be present in a treatment including any mechanism which leads to a dependence of the final state on both the neutrino’s emission and absorption time. Using a simplified model in 1+11+11+1 1 + 1 d, we show that if the positions of the final state particles are measured, or equivalently entangled with the environment, then decoherence will damp neutrino oscillations. We also show that wave packet spreading can cause the decoherence to eventually saturate, without completely suppressing the oscillations. These results are not an artifact of the approximation used: we show that, considering the V−AV-AV−A V - A model in 3+13+13+1 3 + 1 d, the difference would be simply a total multiplicative factor that would not affect the oscillation probability nor the decoherence.
Quantum decoherence in neutrino oscillations was theorized almost 50 years ago, however there is still no clear theoretical understanding of this phenomenon, not even agreement on whether or not it could be observed at all. Treating all particles, including the source and detector, consistently in QFT, we are working on a model where the decoherence emerges from the time evolution of the initial state. We started by studying some simplified cases, obtaining nonetheless interesting results: we have shown that environmental interactions play crucial role in the emergence of decoherence, and if the neutrino creation happens in vacuum there is no maximal coherence length. We have also shown that some of the assumptions commonly used in literature (such as the covariance of the wavepackets) are inconsistent, since the time evolution would break the Lorentz invariance; moreover we have seen that, contrary to the usual intuition, the uncertainty on the detector momentum does not always play a relevant role in decoherence, at least as long as the detector particle is non-relativistic, since its contribution is suppressed by a factor proportional to p/M. Finally, we also notice the emergence of a new quantum effect: when the first neutrinos arrive, the oscillations do not starts immediately but only a very short amount of time; however, since the time window when this effect would be observable is extremely small, the precision required to measure such an effect is most likely well beyond the current technical capabilities
The controversies regarding the oscillation formula are reviewed. The different existing quantum field treatments of oscillations are reconciled by a thorough study of the external wave packet model. Stationary models are shown to be a particular case of this model. All decoherence terms are computed explicitly, so that it becomes clear that the coherence length tends to infinity in the stationary limit. Decoherence is shown to originate not only in the separation of wave packets, but also in their dispersion. Relativistic and nonrelativistic oscillating particles are treated on the same footing. The oscillation formula is derived for an unstable particle within the same formalism. Finally, correlated oscillations are discussed in detail.