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arXiv:1312.2178 · Physica Scripta

On particle oscillations

Marek Góźdź, ANDRZEJ GÓŹDŹ

Published Apr 29, 2014• 3 citations
arXivHTMLPDF

Abstract

It has been firmly established that neutrinos change their flavour during propagation. This feature is attributed to the feature that each flavour eigenstate is a superposition of three mass eigenstates, which propagate with different frequencies. This picture, although widely accepted, is wrong in the simplest approach and requires quite sophisticated treatment based on the wave-packet description within quantum field theory. In this communication we present a novel, much simpler explanation and show that oscillations among massive particles can be obtained in a natural way. We use the framework of quantum mechanics with time being a physical observable, not just a parameter.

DOI
10.1088/0031-8949/89/5/054010

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It has been firmly established that neutrinos change their flavour during propagation. This feature is attributed to the feature that each flavour eigenstate is a superposition of three mass eigenstates, which propagate with different frequencies. This picture, although widely accepted, is wrong in the simplest approach and requires quite sophisticated treatment based on the wave-packet description within quantum field theory. In this communication we present a novel, much simpler explanation and show that oscillations among massive particles can be obtained in a natural way. We use the framework of quantum mechanics with time being a physical observable, not just a parameter.
The theory of neutrino oscillations rests on the assumption, that the interaction basis and the physical (mass) basis of neutrino states are different. Therefore neutrino is produced in a certain welldefined superposition of three mass eigenstates, which propagate separately and may be detected as a different superposition. This is called flavor oscillations. It is, however, not clear why neutrinos behave this way, i.e., what is the underlying mechanism which leads to the production of a superposition of physical states in a single reaction. In this paper we argue, that one of the reasons may be connected with the temporal structure of the process. In order to discuss the role of time in processes on the quantum level, we use a special formulation of the quantum mechanics, which is based on the projection time evolution. We arrive at the conclusion, that for short reaction times the formation of a superposition of states of similar masses is natural.
When neutrinos propagate over long distances, the mass eigenstate components of a flavor eigenstate will become spatially separated due to their different group velocities. This can happen over terrestrial distance scales if the neutrino energy is of order MeV and if the neutrino is localized (in a quantum mechanical sense) to subatomic scales. For example, if the Heisenberg uncertainty in the neutrino position is below 0.01 Angstrom, neutrino decoherence can be observed in reactor neutrinos using a large liquid scintillator detector.
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.
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.
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.
Simple rigorous quantum mechanics with no hand waving nor loopholes clarifies the confusion between three contradictory descriptions of the coherence between different neutrino mass eigenstates that can give rise to oscillations: (1) The standard textbook description of oscillations in time produced by coherence between states with different masses and different energies. (2) Stodolsky's proof that interference between states having different energies cannot be observed in realistic experiments. (3) The description of a pion decay at rest into an observed muon and unobserved neutrino as a “missing mass” experiment where coherence between different neutrino mass eigenstates is not observable. The known position in space of all realistic detectors is rigorously shown to provide the quantum-mechanical ignorance of the neutrino momentum needed to produce coherence between amplitudes from neutrino states with the same energy and different masses. Conditions are precisely formulated for the loss of coherence when mass eigenstate wave packets moving with different velocities separate. The example of Bragg scattering shows how quantum-mechanically imposed ignorance produces coherence.