A diagrammatic treatment of neutrino oscillations

TL;DR

This paper introduces a covariant wave-packet framework using macroscopic Feynman diagrams to analyze neutrino flavor transitions, clarifying the conditions where quantum-mechanical probability applies.

Contribution

It develops a covariant, diagrammatic approach to neutrino oscillations that unifies production, propagation, and detection processes in a single formalism.

Findings

Derives a multidimensional integral expression for transition probability.

Identifies conditions for the flavor transition factor to match quantum-mechanical probability.

Provides a covariant description consistent with relativistic quantum field theory.

Abstract

We present a covariant wave-packet approach to neutrino flavor transitions in vacuum. The approach is based on the technique of macroscopic Feynman diagrams describing the lepton number violating processes of production and absorption of virtual massive neutrinos at the macroscopically separated space-time regions ("source" and "detector"). Accordingly, the flavor transitions are a result of interference of the diagrams with neutrinos of different masses in the intermediate states. The statistically averaged probability of the process is representable as a multidimensional integral of the product of the factors which describe the differential flux density of massless neutrinos from the source, differential cross section of the neutrino interaction with the detector and a dimensionless factor responsible for the flavor transition. The conditions are analyzed under which the last factor can be treated as the flavor transition probability in the usual quantum-mechanical sense.