Lepton number crossings are insufficient for flavor instabilities

TL;DR

This paper demonstrates that spectral crossings in dense neutrino environments are not always sufficient for flavor instabilities, providing a counterexample and explaining the physical mechanism behind it.

Contribution

The authors construct a counterexample showing spectral crossings can occur without instabilities, challenging previous assumptions in neutrino flavor physics.

Findings

Spectral crossings are not always sufficient for flavor instabilities.

An explicit counterexample with an even number of crossings is provided.

Flavor wave growth depends on the dominance of flipped-lepton-number neutrinos.

Abstract

In dense neutrino environments, the mean field of flavor coherence can develop instabilities. A necessary condition is that the flavor lepton number changes sign as a function of energy and/or angle. Whether such a crossing is also sufficient has been a longstanding question. We construct an explicit counterexample: a spectral crossing without accompanying flavor instability, with an even number of crossings being key. This failure is physically understood as Cherenkov-like emission of flavor waves. If flipped-lepton-number neutrinos never dominate among those kinematically allowed to decay, the waves cannot grow.