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Oscillations of neutrinos and mesons in quantum field theory

Beuthe, M

Published Jan 1, 2001• 162 citations
OpenAlex

Abstract

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.

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The problem of particle oscillation is considered in a pedagogical and comprehensive way. Examples from K, B and neutrino physics are given. Conceptual difficulties of the traditional approach to particle oscillation are discussed. It is shown how the probability current density and the wave packet treatments of particle oscillations resolve some problems. It is also shown that only full field theoretical approach is free from conceptual difficulties. The possibility of oscillation of particles produced together with kaons or neutrinos is considered in full wave packet quantum mechanics language. Precise definition of the oscillation of particles which recoil against mixed states is given. The general amplitude which describes the oscillation of two particles in the final states is found. Using this EPR-type amplitude the problem of oscillation of particles recoiling against kaons or neutrinos is resolved. The relativistic EPR correlations on distances of the order of coherence lengths are considered.
A quantum wave packet treatment of neutrino and neutral K and B meson oscillations is presented which incorporates the recoil particle in the production process, and includes the effect of the localization and lifetime of the source assumed to be a resonance or unstable particle. This approach removes the ambiguities in the conventional single particle treatment of these oscillations with the recoil particle. A fundamental connection between the stochastic decay time of the source and the space-time coordinates of the correlated final state particles is derived.
We perform such a calculation in quantum field theory, where we include simultaneously the source, detector, and neutrino fields in the Hamiltonian. Within the appropriate limits associated with current neutrino oscillation experiments, we recover the standard oscillation formula. On the other hand, we find that the dominant contributions to the amplitude are associated with different neutrino mass eigenstates being emitted at different times, such that they arrive at the detector at the same time. This is contrary to the neutrino wave packet picture, where they are emitted simultaneously and separate as they travel to the detector. This has direct consequences regarding the mechanisms that lead to a damping of neutrino oscillations for very long baselines. Our analysis also provides a pedagogical example of a measurement process in quantum mechanics.
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Abstract Quantum correlations provide a fertile testing ground for investigating fundamental aspects of quantum physics in various systems, especially in the case of relativistic (elementary) particle systems as neutrinos. In a recent paper, Ming et al. (Eur Phys J C 80:275, 2020), in connection with results of Daya-Bay and MINOS experiments, have studied the quantumness in neutrino oscillations in the framework of plane-wave approximation. We extend their treatment by adopting the wave packet approach that accounts for effects due to localization and decoherence. This leads to a better agreement with experimental results, in particular for the case of MINOS experiment.