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arXiv:2307.12230 · Physics Letters B

Decoherence in neutrino oscillation between 3D Gaussian wave packets

Haruhi Mitani, Kin-ya Oda

Published Oct 2, 2023• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1016/j.physletb.2023.138218

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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.
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.
We theoretically explore the possibility of observing the quantum decoherence of neutrino oscillation due to the vacuum dispersion, that the wave-packet of neutrino spatially splits according to the different velocities of two mass eigenstates. We find that if this decoherence could be observed and the range of values of the mixing angle is known, then the superluminal neutrino phenomena could occur for some mixing angles as the consequence of a weak measurement about flavor mixing in the neutrino propagation. Our calculation gives the explicit dependence of group velocity shift to the decoherence factor and the weak value of neutrino's pre and post-selected states. We also study the related problems for the neutrino oscillation with three generations.
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.
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.