Fast Flavor Pendulum: Instability Condition

TL;DR

This paper investigates the conditions under which a neutrino gas exhibits fast flavor instability, focusing on the dispersion relation and the role of critical points, with implications for understanding neutrino oscillations.

Contribution

It extends the analysis of flavor instability conditions by exploring the dispersion relation for modes with arbitrary wave number and clarifies the limitations of previous graphical methods.

Findings

Homogeneous flavor instability can be analyzed using a Nyquist criterion.

Superluminal critical points complicate the simple instability condition.

The homogeneous mode's role is limited to its long-term behavior and symmetries.

Abstract

Even in the absence of neutrino masses, a neutrino gas can exhibit a homogeneous flavor instability that leads to a periodic motion known as the fast flavor pendulum. A well-known necessary condition is a crossing of the angular flavor lepton distribution. In an earlier work, some of us showed that homogeneous flavor instabilities also obey a Nyquist criterion, inspired by plasma physics. This condition, while more restrictive than the angular crossing, is only sufficient if the unstable branch of the dispersion relation is bounded by critical points that both lie under the light cone (points with subluminal phase velocity). While the lepton-number angle distribution, assumed to be axially symmetric, easily allows one to determine the real-valued branch of the dispersion relation and to recognize if instead superluminal critical points exist, this graphical method does not translate into a simple instability condition. We discuss the homogeneous mode in the more general context of the dispersion relation for modes with arbitrary wave number and stress that it plays no special role on this continuum, except for its regular but fragile long-term behavior, owed to its many symmetries.