Entanglement in three-flavor collective neutrino oscillations

TL;DR

This paper presents the first three-flavor many-body calculations of collective neutrino oscillations, highlighting the importance of quantum entanglement and its dependence on mass ordering in supernova environments.

Contribution

It introduces a novel three-flavor many-body approach to neutrino oscillations and quantifies entanglement, revealing limitations of two-flavor approximations.

Findings

Entanglement can be underestimated in two-flavor models.

Entanglement varies with neutrino mass ordering.

Mass eigenstate mixing depends on the mass hierarchy.

Abstract

Extreme conditions present in the interiors of the core-collapse supernovae make neutrino-neutrino interactions not only feasible but dominant in specific regions, leading to the non-linear evolution of the neutrino flavor. Results obtained when such collective neutrino oscillations are treated in the mean-field approximation deviate from the results using the many-body picture because of the ignored quantum correlations. We present the first three flavor many-body calculations of the collective neutrino oscillations. The entanglement is quantified in terms of the entanglement entropy and the components of the polarization vector. We propose a qualitative measure of entanglement in terms of flavor-lepton number conserved quantities. We find that in the cases considered in the present work, the entanglement can be underestimated in two flavor approximation. The dependence of the entanglement on mass ordering is also investigated. We also explore the mixing of mass eigenstates in different mass orderings.