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arXiv:2205.05367 · The European Physical Journal C

Where neutrino decoherence lies

Emilio Ciuffoli, Jarah Evslin

Published Dec 6, 2022• 3 citations
arXivHTMLPDF

Abstract

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 $$1+1$$ 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 $$V-A$$ V - A model in $$3+1$$ 3 + 1 d, the difference would be simply a total multiplicative factor that would not affect the oscillation probability nor the decoherence.

DOI
10.1140/epjc/s10052-022-11090-6

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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.
Abstract It is well known that neutrino oscillations may damp due to decoherence caused by the separation of mass eigenstate wave packets or by a baseline uncertainty of order the oscillation wave length. In this note we show that if the particles created together with the neutrino are not measured and do not interact with the environment, then the first source of decoherence is not present. This demonstration uses the saddle point approximation and also assumes that the experiment lasts longer than a certain threshold. We independently derive this result using the external wave packet model and also using a model in which the fields responsible for neutrino production and detection are treated dynamically. Intuitively this result is a consequence of the fact that the neutrino emission time does not affect the final state and so amplitudes corresponding to distinct emission times must be added coherently. This fact also implies that oscillations resulting from mass eigenstates which are detected simultaneously arise from neutrinos which were not created simultaneously but are nonetheless coherent, realizing the neutrino oscillation paradigm of Kobach, Manohar and McGreevy.
I will present some of the results obtained regarding the emergence of decoherence in neutrino oscillations. In our model all the particles, including the source and detector, are treated dynamically and evolved consistently with Quantum Field Theory; decoherence can emerge naturally given the time evolution of the initial state and the final state considered. We have shown that some of the assumptions commonly used in the literature, such as the covariance of the wavepackets, are inconsistent. We found that a crucial ingredient for decoherence is the localization in space-time of the neutrino creation and detection: in Nature, such a measurement is usually carried out by environmental interactions, however it could also be approximated by considering localized wavefunctions in the final state. On the other hand, if the environmental interactions are not present (for example, if the decay happens in vacuum), the final position of the daughter particles will not be measured, i.e. they will be described by plane waves instead: in this case the neutrino is not localized either, and we don't have decoherence. A consequence of the time-evolution is that a Gaussian wavepacket will gradually spread: I will show that such an effect could in principle affect decoherence; moreover it would depend on the absolute mass scale of the neutrino, not on the Δm2\Delta m^2Δm2, which could offer a possible way to probe such a parameter by studying the neutrino oscillations.
We point out three apparent inconsistencies in the treatment of oscillation coherence from reactor neutrino and source neutrino experiments in recent paper "Damping of neutrino oscillations, decoherence and the lengths of neutrino wave packets''. First, that the dependence of the oscillation probability upon the subsequent interactions of entangled recoil particles implies causality violations and in some situations superluminal signaling; second, that integrating over a non-orthogonal basis for the entangled recoil leads to unphysical effects; and third, that the question of what interactions serve to measure the position of the initial state particle remains ambiguous. These points taken together appear to undermine the claim made therein that the effects of wave packet separation must be strictly unobservable in reactor and radioactive source based neutrino experiments.
It has been claimed that wave packets must be covariant and also that decohered neutrino oscillations are always revived during measurement. These conjectures are supported by general arguments which are not specific to the electroweak theory, and so if they are true for neutrinos they will also be true for simplified models. In this paper we produce such a simplified model in which the neutrino wave function, including its entanglement with the source particle and the environment, can be calculated explicitly in quantum field theory. It exhibits neutrino oscillation, which is reduced at late times by decoherence due to interactions of the source with the environment. One simple lesson from this model is that only the difference between the environmental interactions before and after neutrino emission can reduce the amplitude of neutrino oscillations. The model will be used to test the conjectures in a companion paper.
It has been claimed that wave packets must be covariant and also that decohered neutrino oscillations are always revived during measurement. These conjectures are supported by general arguments which are not specific to the electroweak theory, and so if they are true for neutrinos they will also be true for simplified models. In this paper we produce such a simplified model in which the neutrino wave function, including its entanglement with the source particle and the environment, can be calculated explicitly in quantum field theory. It exhibits neutrino oscillation, which is reduced at late times by decoherence due to interactions of the source with the environment. One simple lesson from this model is that only the difference between the environmental interactions before and after neutrino emission can reduce the amplitude of neutrino oscillations. The model will be used to test the conjectures in a companion paper.
Abstract Spatial separation of the wave packets (WPs) of neutrino mass eigenstates leads to decoherence and damping of neutrino oscillations. Damping can also be caused by finite energy resolution of neutrino detectors or, in the case of experiments with radioactive neutrino sources, by finite width of the emitted neutrino line. We study in detail these two types of damping effects using reactor neutrino experiments and experiments with radioactive 51Cr source as examples. We demonstrate that the effects of decoherence by WP separation can always be incorporated into a modification of the energy resolution function of the detector and so are intimately entangled with it. We estimate for the first time the lengths σx of WPs of reactor neutrinos and neutrinos from a radioactive 51Cr source. The obtained values, σx = (2 × 10−5 − 1.4 × 10−4) cm, are at least six orders of magnitude larger than the currently available experimental lower bounds. We conclude that effects of decoherence by WP separation cannot be probed in reactor and radioactive source experiments.