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

TL;DR

This paper introduces a dispersion relation approach to analyze fast pairwise neutrino conversions in supernovae, revealing conditions for instability and flavor coherence disturbances.

Contribution

A novel dispersion relation method is developed to understand fast neutrino pair conversions and their dependence on initial conditions in supernova environments.

Findings

Identification of dispersion gaps where instabilities occur

Demonstration of the role of initial conditions in flavor coherence

Insight into the conditions for fast neutrino flavor conversions

Abstract

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.