Fast Pairwise Conversion of Supernova Neutrinos: A Dispersion Relation Approach

Collective pair conversion v(e)(v) over bar (e)<-> v(x)(v) over bar (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 can be "fast," i.e., of the order of root 2G(F)(n(ve) - n((v) over bare)) >> Delta m(atm)(2)/2E. We present a novel approach to understand these phenomena: a dispersion relation for the frequency and wave number (Omega, Kappa) of disturbances in the mean field of v(e)v(x) flavor coherence. Runaway solutions occur in "dispersion gaps," i.e., in "forbidden" intervals of Omega and/or (K) over bar 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.