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Lepton-Number Crossings are Insufficient for Flavor Instabilities

Damiano F. G. Fiorillo1 and Georg G. Raffelt2

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Phys. Rev. Lett. 136, 051001 – Published 3 February, 2026

DOI: https://doi.org/10.1103/d629-bh5y

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.

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Phys. Rev. Lett. 136, 051001– Published 3 February, 2026
  • Received 3 August 2025
  • Revised 13 December 2025
  • Accepted 2 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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