Neutrino oscillations: Quantum mechanics vs. quantum field theory

TL;DR

This paper compares quantum mechanics and quantum field theory approaches to neutrino oscillations, deriving connections between their parameters and demonstrating how proper normalization of oscillation probabilities is achieved in QFT.

Contribution

It provides a detailed comparison between QM and QFT treatments of neutrino oscillations, deriving QM wave packets from QFT and clarifying parameter relations.

Findings

Derived QM neutrino wave packets from QFT

Connected effective momentum uncertainty to fundamental QFT parameters

Showed proper normalization of oscillation probabilities in QFT

Abstract

A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.