Plane-wave model of neutrino oscillations revisited

TL;DR

This paper re-examines the plane-wave model of neutrino oscillations, demonstrating that the standard oscillation formulae can be derived without unphysical assumptions by properly defining interference conditions.

Contribution

It shows that the standard neutrino oscillation formulas can be obtained from a plane-wave model without unphysical assumptions, using a heuristic approach based on coherence and proper interference definitions.

Findings

Standard oscillation formulas derived without unphysical assumptions

Interference at time t = L/β justified by coherence arguments

Plane-wave model can be consistent with physical principles

Abstract

The phenomenology of massive neutrinos -- flavour mixing in the lepton sector causing oscillations between different neutrino-types along their propagation over macroscopic distances in vacuum -- aims at relating observable quantities (oscillation frequency or, equivalently, oscillation length) to the neutrino properties: mixing angles $\theta_{ij}$ and mass-squared differences $\Delta m_{ij}^2$. Calculation of the probabilities for a given neutrino-type either to survive or to mutate into another type, as functions of momentum $p$ and travelling distance $L$, are properly based on wave-packet models of varying complexity. Approximations neglecting subtle effects like decoherence result in the standard oscillation formulae with terms proportional to $\sin^2(\Delta m_{ij}^2 L / 4 p)$. The same result may also be derived by a simple plane-wave model as shown in most textbooks. However, those approaches rely on unphysical a-priory assumptions: either "equal energy" or "equal velocity" or "equal momentum" in the phases of different mass eigenstates -- which are refuted elsewhere. In addition, some assume tacitly that interference occurs at time $t = L$. This study re-examines the plane-wave model. No unphysical assumption is necessary for deriving the standard formulae: a heuristic approach relies only on carefully defining interference at time $t = L / \beta$, and is justified by coherence arguments based in a qualitative way on wave-packets.