Collective three-flavor oscillations of supernova neutrinos

TL;DR

This paper develops a comprehensive three-flavor formalism for supernova neutrino oscillations, revealing how collective effects can be understood through factorization into two-flavor oscillations and visualized with a triangle diagram.

Contribution

It introduces a generalized formalism for three-flavor neutrino oscillations in supernovae, enabling analytical descriptions of complex collective phenomena and their interplay with MSW effects.

Findings

Flavor conversions can be factorized into two-flavor oscillations.

The formalism describes phenomena like bipolar and spectral split.

The triangle diagram visualizes three-flavor effects.

Abstract

Neutrinos and antineutrinos emitted from a core collapse supernova interact among themselves, giving rise to collective flavor conversion effects that are significant near the neutrinosphere. We develop a formalism to analyze these collective effects in the complete three-flavor framework. It naturally generalizes the spin-precession analogy to three flavors and is capable of analytically describing phenomena like vacuum/MSW oscillations, synchronized oscillations, bipolar oscillations and spectral split. Using the formalism, we demonstrate that the flavor conversions may be "factorized" into two-flavor oscillations with hierarchical frequencies. We explicitly show how the three-flavor solution may be constructed by combining two-flavor solutions. For a typical supernova density profile, we identify an approximate separation of regions where distinctly different flavor conversion mechanisms operate, and demonstrate the interplay between collective and MSW effects. We pictorialize our results in terms of the "e_3 - e_8 triangle" diagram, which is a tool that can be used to visualize three-neutrino flavor conversions in general, and offers insights into the analysis of the collective effects in particular.