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arXiv:1711.07491 · Physics Letters B

Neutrino oscillation measurements computed in quantum field theory

Andrew Kobach, Aneesh V. Manohar, John McGreevy

Published Jun 21, 2018• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1016/j.physletb.2018.06.021

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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.
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.
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.
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.
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
We consider a quantum field theory (QFT) model of neutrino oscillations in vacuum that attempts to take into account that the neutrino source particle and the neutrino detection particle both interact with their respective environments by collisions. Our model is minimal in a twofold sense. Firstly we simply assume that neutrino production and detection take place in between collisions in time intervals ΔtΔtΔt and τττ, respectively. Secondly, we only introduce the two wave packets that are absolutely necessary which are those of the neutrino source and the neutrino detection particle. Within this model we find that, for all practical purposes, there are no decoherence effects in the neutrino oscillation amplitude and oscillations occur in space not in time. Moreover, our model leads to the correct time correlation between neutrino production and detection and to a factorization of the event rate of the compound neutrino production--detection process into decay rate, oscillation probability and detection cross section.
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.