Theory of neutrino fast flavor evolution. Part I. Linear response theory and stability conditions

TL;DR

This paper develops a linear response theoretical framework for fast neutrino flavor conversion in supernovae, predicting growth modes and damping effects, and clarifies conditions for collective neutrino oscillations.

Contribution

It introduces a flavor susceptibility concept and a new dispersion relation that accounts for Landau damping, enhancing understanding of neutrino flavor evolution.

Findings

Identifies angular crossings as triggers for growing modes.

Predicts Landau damping of subluminal modes.

Provides a simplified, intuitive explanation for mode growth conditions.

Abstract

Neutrino-neutrino refraction leads to collective flavor evolution that can include fast flavor conversion, an ingredient still missing in numerical simulations of core-collapse supernovae. We provide a theoretical framework for the linear regime of this phenomenon using the language of response theory. In analogy to electromagnetic waves, we introduce a flavor susceptibility as the linear response to an external flavor field. By requiring self-consistency, this approach leads to the usual dispersion relation for growing modes, but differs from the traditional treatment in that it predicts Landau damping of subluminal collective modes. The new dispersion relation has definite analyticity properties and can be expanded for small growth rates. This approach simplifies and intuitively explains Morinaga's proof of sufficiency for the occurrence of growing modes. We show that weakly growing modes arise as soon as an angular crossing is formed, due to their resonant interaction with individual neutrino modes. For longitudinal plasma waves, a similar resonance causes Landau damping or conversely, the two-stream instability.