# Fast Neutrino Flavor Conversion: Collective Motion vs. Decoherence

## TL;DR

This paper investigates the dynamics of neutrino flavor conversion, revealing the coexistence of collective and non-collective modes, and identifying conditions that lead to tachyonic instabilities in dense neutrino gases.

## Contribution

It provides a detailed analysis of the dispersion relation for fast neutrino flavor modes, including explicit eigenfunctions and conditions for instabilities based on angular mode crossings.

## Key findings

- Existence of a continuum of non-collective modes alongside discrete collective modes.
- Single angular crossings lead to tachyonic instabilities, while multiple crossings may not.
- Explicit eigenfunctions for both collective and non-collective modes are derived.

## Abstract

In an interacting neutrino gas, flavor coherence becomes dynamical and can propagate as a collective mode. In particular, tachyonic instabilities can appear, leading to "fast flavor conversion" that is independent of neutrino masses and mixing angles. On the other hand, without neutrino-neutrino interaction, a prepared wave packet of flavor coherence simply dissipates by kinematical decoherence of infinitely many non-collective modes. We reexamine the dispersion relation for fast flavor modes and show that for any wavenumber,there exists a continuum of non-collective modes besides a few discrete collective ones. So for any initial wave packet, both decoherence and collective motion occurs, although the latter typically dominates for a sufficiently dense gas. We derive explicit eigenfunctions for both collective and non-collective modes. If the angular mode distribution of electron-lepton number crosses between positive and negative values, two non-collective modes can merge to become a tachyonic collective mode. We explicitly calculate the interaction strength for this critical point. As a corollary we find that a single crossing always leads to a tachyonic instability. For an even number of crossings, no instability needs to occur.