Lepton number crossings are insufficient for flavor instabilities

Understand

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.