Neutrino oscillations in Quantum Field Theory

TL;DR

This paper develops a Quantum Field Theory framework for neutrino oscillations, deriving a process-dependent formula that generalizes the conventional probability-based approach and clarifies the underlying quantum field dynamics.

Contribution

It introduces a QFT-based method for neutrino oscillations that models emission, detection, and propagation within a unified diagrammatic approach, extending beyond traditional quantum mechanics models.

Findings

Derived an $L$-dependent master formula for neutrino production rate.

Showed the QFT formula can approximate conventional oscillation probabilities.

Clarified the process-dependent nature of neutrino oscillations in QFT.

Abstract

We propose a Quantum Field Theory (QFT) approach to neutrino oscillations in vacuum. The neutrino emission and detection are identified with the charged-current vertices of a single second-order Feynman diagram for the underlying process, enclosing neutrino propagation between these two points. The key point of our approach is the definition of the space-time setup typical for neutrino oscillation experiments, implying macroscopically large but finite volumes of the source and detector separated by a sufficiently large distance $L$. We derive an $L$-dependent master formula for the charged lepton production rate, which provides the QFT basis for the analysis of neutrino oscillations. Our formula depends on the underlying process and is not reducible to the conventional approach resorting to the concept of neutrino oscillation probability, which originates from non-relativistic quantum mechanics (QM). We demonstrate that for some particular choice of the underlying process our QFT formula approximately coincides with the conventional one under some assumptions.