Simultaneous Flavor Transformation of Neutrinos and Antineutrinos with Dominant Potentials from Neutrino-Neutrino Forward Scattering

In astrophysical environments with intense neutrino fluxes, neutrino-neutrino forward scattering contributes both diagonal and off-diagonal potentials to the flavor-basis Hamiltonian that governs neutrino flavor evolution. We examine a special case where adiabatic flavor evolution can produce an off-diagonal potential from neutrino-neutrino forward scattering that dominates over both the corresponding diagonal term and the potential from neutrino-matter forward scattering. In this case, we find a solution that, unlike the ordinary Mikeyhev-Smirnov-Wolfenstein scenario, has both neutrinos and antineutrinos maximally mixed in medium over appreciable ranges of neutrino and antineutrino energy. Employing the measured solar and atmospheric neutrino mass-squared differences, we identify the conditions on neutrino fluxes that are required for this solution to exist deep in the supernova environment, where it could affect the neutrino signal, heavy-element nucleosynthesis, and even the revival of the supernova shock. We speculate on how this solution might or might not be attained in realistic supernova evolution. Though this solution is ephemeral in time and/or space in supernovae, it may signal the onset of subsequent appreciable flavor mixing for both neutrinos and antineutrinos. A similar solution may also exist in an early universe with significant net neutrino-lepton numbers.