Paradoxes of neutrino oscillations

TL;DR

This paper critically examines foundational issues in neutrino oscillation theory using a wave packet approach, addressing debates on assumptions, coherence, Lorentz invariance, and proposing a novel calculation method.

Contribution

It introduces a new wave packet-based method for calculating oscillation probabilities and clarifies several paradoxical aspects of neutrino oscillation theory.

Findings

Reveals limitations of the 'same energy' and 'same momentum' assumptions.

Shows coherence conditions depend on energy and momentum uncertainties.

Proposes a novel calculation approach offering new phenomenological insights.

Abstract

Despite the theory of neutrino oscillations being rather old, some of its basic issues are still being debated in the literature. We discuss, in the framework of the wave packet approach, a number of such issues, including the relevance of the "same energy" and "same momentum" assumptions, the role of quantum-mechanical uncertainty relations in neutrino oscillations, the dependence of the production/detection and propagation coherence conditions that ensure the observability of neutrino oscillations on neutrino energy and momentum uncertainties, the question of (in)dependence of the oscillation probabilities on the neutrino production and detection processes, the applicability limits of the stationary source approximation, and Lorentz invariance of the oscillation probability. We also develop a novel approach to calculation of the oscillation probability in the wave packet picture, based on the summation/integration conventions different from the standard one, which gives a new insight into the oscillation phenomenology. We discuss a number of apparently paradoxical features of the theory of neutrino oscillations.