{
  "id": "2312.06556",
  "version": "v1",
  "published": "2023-12-11T17:43:30.000Z",
  "updated": "2023-12-11T17:43:30.000Z",
  "title": "Fast Conversion of Neutrinos: Energy Dependence of Flavor Instabilities",
  "authors": [
    "Pedro Dedin Neto",
    "Irene Tamborra",
    "Shashank Shalgar"
  ],
  "comment": "16 pages, including 5 figures and 1 appendix",
  "categories": [
    "astro-ph.HE"
  ],
  "abstract": "In core-collapse supernovae and neutron star mergers, the neutrino density is so large that neutrino-neutrino refraction can lead to flavor conversion, classified as ``fast'' since the neutrino self-interaction strength $\\mu=\\sqrt{2} G_F n_\\nu$ represents the characteristic time-scale of the system. However, it has been empirically realized that the vacuum frequency $\\omega=\\Delta m^2/2E$ affects the development of flavor conversion even if $\\omega \\ll \\mu$, as is the case in the core of compact astrophysical sources. Focusing on a homogeneous and axially symmetric neutrino gas, we explore the role of $\\omega$ in the onset of flavor instabilities. Relying on a perturbative approach, we find that the odd powers of $\\omega$ are linked to the angular distribution of the neutrino flavor particle number (FPN). Hence, when $\\omega \\neq 0$, the flavor conversion dynamics does not depend on the neutrino flavor lepton number only (FLN), like for fast flavor conversion, but also on the FPN. A non-zero vacuum frequency is also responsible for inducing flavor instabilities with a non-negligible growth rate in a neutrino gas that would be otherwise stable for $\\omega \\rightarrow 0$. Such a neutrino ensemble with $\\omega \\neq 0$ can be formally mapped into an effective system with $\\omega =0$, whose angular distributions have non-zero imaginary components. Our work highlights the overlooked role of vacuum mixing in the development of flavor instabilities in neutrino systems with FLN zero-crossings in the angular distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-11T17:43:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "flavor instabilities",
      "energy dependence",
      "fast conversion",
      "angular distribution",
      "neutrino flavor particle number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}