Neutrino flavor pendulum in both mass hierarchies

TL;DR

This paper demonstrates that in dense neutrino gases, collective flavor oscillations can break initial symmetries, revealing new instabilities in the normal hierarchy that were previously unrecognized.

Contribution

It introduces a simple model showing symmetry-breaking solutions in neutrino flavor evolution, highlighting the existence of a new instability in the normal hierarchy.

Findings

Symmetry-breaking solutions exist in neutrino flavor oscillations.

A new instability occurs in the normal hierarchy when initial symmetries are lifted.

The results relate to the multi-azimuth angle instability in supernova neutrino fluxes.

Abstract

We construct a simple example for self-induced flavor conversion in dense neutrino gases showing new solutions that violate the symmetries of initial conditions. Our system consists of two opposite momentum modes 1 and 2, each initially occupied with equal densities of nu_e and anti-nu_e. Restricting solutions to symmetry under 1 <-> 2 allows for the usual bimodal instability ("flavor pendulum") in the inverted neutrino mass hierarchy (IH) and stability (no self-induced flavor conversion) in the normal hierarchy (NH). Lifting this symmetry restriction allows for a second pendulum-like solution that occurs in NH where the modes 1 and 2 swing in opposite directions in flavor space. Any small deviation from 1-2 symmetry in the initial condition triggers the new instability in NH. This effect corresponds to the recently identified multi-azimuth angle (MAA) instability of supernova neutrino fluxes. Both cases show explicitly that solutions of the equations of collective flavor oscillations need not inherit the symmetries of initial conditions, although this has been universally assumed.