Neutrino oscillations: Entanglement, energy-momentum conservation and QFT

TL;DR

This paper clarifies the quantum field theory description of neutrino oscillations, emphasizing the importance of space-time localization, coherence, and entanglement, and shows the equivalence of different calculation approaches.

Contribution

It demonstrates that proper quantum field theory conditions can accurately describe neutrino oscillations, resolving debates on energy-momentum conservation and entanglement effects.

Findings

Space-time localization is crucial for neutrino oscillation coherence.

Two calculation methods are equivalent in describing oscillations.

Recoil particle contributions are negligible under coherence conditions.

Abstract

We consider several subtle aspects of the theory of neutrino oscillations which have been under discussion recently. We show that the $S$-matrix formalism of quantum field theory can adequately describe neutrino oscillations if correct physics conditions are imposed. This includes space-time localization of the neutrino production and detection processes. Space-time diagrams are introduced, which characterize this localization and illustrate the coherence issues of neutrino oscillations. We discuss two approaches to calculations of the transition amplitudes, which allow different physics interpretations: (i) using configuration-space wave packets for the involved particles, which leads to approximate conservation laws for their mean energies and momenta; (ii) calculating first a plane-wave amplitude of the process, which exhibits exact energy-momentum conservation, and then convoluting it with the momentum-space wave packets of the involved particles. We show that these two approaches are equivalent. Kinematic entanglement (which is invoked to ensure exact energy-momentum conservation in neutrino oscillations) and subsequent disentanglement of the neutrinos and recoiling states are in fact irrelevant when the wave packets are considered. We demonstrate that the contribution of the recoil particle to the oscillation phase is negligible provided that the coherence conditions for neutrino production and detection are satisfied. Unlike in the previous situation, the phases of both neutrinos from $Z^0$ decay are important, leading to a realization of the Einstein-Podolsky-Rosen paradox.