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Abstract

Neutrino-neutrino refraction in dense media can cause self-induced flavor conversion triggered by collective run-away modes of the interacting flavor oscillators. The growth rates were usually found to be of order a typical vacuum oscillation frequency $\Delta m^2/2E$. However, even in the simple case of a $\nu_e$ beam interacting with an opposite-moving $\bar\nu_e$ beam, and allowing for spatial inhomogeneities, the growth rate of the fastest-growing Fourier mode is of order $\mu=\sqrt{2} G_{\rm F} n_{\nu}$, a typical $\nu$--$\nu$ interaction energy. This growth rate is much larger than the vacuum oscillation frequency and gives rise to flavor conversion on a much shorter time scale. This phenomenon of "fast flavor conversion" occurs even for vanishing $\Delta m^2/2E$ and thus does not depend on energy, but only on the angle distributions. Moreover, it does not require neutrinos to mix or to have masses, except perhaps for providing seed disturbances. We also construct a simple homogeneous example consisting of intersecting beams and study a schematic supernova model proposed by Ray Sawyer, where $\nu_e$ and $\bar\nu_e$ emerge with different zenith-angle distributions, the key ingredient for fast flavor conversion. What happens in realistic astrophysical scenarios remains to be understood.