On Neutrino Flavor States

TL;DR

This paper critically examines the nature of neutrino flavor states, arguing they are not physical states but useful definitions, especially relevant when neutrinos are ultra-relativistic or have negligible mass differences.

Contribution

It provides a rigorous proof that neutrino flavor states are approximately well-defined only under specific conditions and clarifies their role as linear combinations of mass eigenstates rather than physical states.

Findings

Flavor states are not physical quantum states.

Weak interactions are described by neutrino mass eigenstates.

Flavor states are useful definitions, not physical states.

Abstract

We review the issues associated with the construction of neutrino flavor states. We then provide a consistent proof that the flavor states are approximately well-defined only if neutrinos are ultra-relativistic or the mass differences are negligible compared to energy. However, we show that weak interactions can be consistently described by only neutrino mass eigenstates. Meanwhile, the second quantization of neutrino flavor fields generally has no physical relevance as their masses are indefinite. Therefore, the flavor states are not physical quantum states and they should simply be interpreted as definitions to denote specific linear combinations of mass eigenstates involved in weak interactions. We also briefly discuss the implication of this work for the mixing between active and heavy sterile neutrinos.