Fast neutrino flavor instability and neutrino flavor lepton number crossings

TL;DR

This paper proves that the presence of neutrino flavor lepton number crossings is both necessary and sufficient for fast neutrino flavor instability, clarifying a key aspect of dense neutrino flavor evolution.

Contribution

It establishes the equivalency between fast neutrino flavor instability and NFLN crossings, resolving previous uncertainties about their relationship.

Findings

NFLN crossings are necessary for fast instability.

NFLN crossings are sufficient for fast instability.

Clarifies the role of NFLN crossings in dense neutrino environments.

Abstract

In this paper, we show the equivalency between the existence of fast neutrino flavor instability and that of neutrino flavor lepton number (NFLN) crossings, which indicates that an NFLN angular distribution takes both signs. The veracity of this proposition has been uncertain and sometimes controversial despite its indispensability in the flavor evolutions of dense neutrinos. This study clarifies that the occurrence of an NFLN crossing is both necessary and sufficient for fast instability.