Quantum field theoretic approach to neutrino oscillations in matter

TL;DR

This paper develops a quantum field theoretic framework for neutrino oscillations in matter, clarifying the conditions for defining oscillation probabilities and highlighting limitations of the Schr"odinger-like evolution in certain scenarios.

Contribution

It introduces a unified QFT approach to neutrino oscillations in non-uniform matter, deriving evolution equations and identifying when standard methods are inadequate.

Findings

Properly normalized oscillation probability can be derived in QFT.

Schr"odinger-like evolution equations are not always applicable, especially with sterile neutrinos.

Conditions for defining oscillation probabilities in a QFT framework are established.

Abstract

We consider neutrino oscillations in non-uniform matter in a quantum field theoretic (QFT) approach, in which neutrino production, propagation and detection are considered as a single process. We find the conditions under which the oscillation probability can be sensibly defined and demonstrate how the properly normalized oscillation probability can be obtained in the QFT framework. We derive the evolution equation for the oscillation amplitude and discuss the conditions under which it reduces to the standard Schr\"odinger-like evolution equation. It is shown that, contrary to the common usage, the Schr\"odinger-like evolution equation is not applicable in certain cases, such as oscillations of neutrinos produced in decays of free pions provided that sterile neutrinos with $\Delta m^2\gtrsim 1$ eV$^2$ exist.