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 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+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.
The initial configuration of a neutrino experiment consists of wave packets, created by the experimenter. Unmeasured final states are essentially delocalized, but it is conventional to nonetheless treat them as localized wave packets as they are in a sense measured by the environment. In this note we consider an experiment in the vacuum, and so there is no environment and the unmeasured final states are not localized. We introduce a simplified but consistent model of neutrino interactions and numerically evolve the system over a finite time using the Hamiltonian to obtain the oscillation probability. All particles involved in neutrino production or detection, localized or not, are treated and evolved consistently in quantum field theory, keeping all entanglements.
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 Δt and τ, 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.
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.
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.
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