Fast Pairwise Conversion of Supernova Neutrinos: A Dispersion-Relation Approach

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Collective pair conversion $\nu_e\bar\nu_e\leftrightarrow \nu_{x}\bar\nu_{x}$ by forward scattering, where $x=\mu$ or $\tau$, may be generic for supernova neutrino transport. Depending on the local angular intensity of the electron lepton number carried by neutrinos, the conversion rate is "fast," i.e., of the order of $\sqrt{2}G_{\rm{F}}(n_{\nu_e}{-}\,n_{\bar\nu_e})\gg\Delta m^2_{\rm atm}/2E$. We present a novel approach to understand these phenomena: A dispersion relation for the frequency and wave number $(\Omega,\bf{K})$ of disturbances in the mean field of $\nu_e\nu_x$ flavor coherence. Run-away solutions occur in "dispersion gaps," i.e., in "forbidden" intervals of $\Omega$ and/or $\bf{K}$ where propagating plane waves do not exist. We stress that the actual solutions also depend on the initial and/or boundary conditions which need to be further investigated.
Original languageEnglish
Article number021101
JournalPhysical Review Letters
Volume118
ISSN0031-9007
DOIs
Publication statusPublished - 10 Jan 2017

Bibliographical note

6 pages, 3 figures. Minor changes in the text, references added and discussion of figure 3 extended. Matches published PRL version

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