We present results of large-scale numerical simulations of the evolution of neutrino and antineutrino flavors in the region above the late-time post-supernova-explosion proto-neutron star. Our calculations are the first to allow explicit flavor evolution histories on different neutrino trajectories and to self-consistently couple flavor development on these trajectories through forward scatteringinduced quantum coupling. Employing the atmospheric-scale neutrino mass-squared difference (|δm 2 | ≃ 3 × 10 −3 eV 2 ) and values of θ13 allowed by current bounds, we find transformation of neutrino and antineutrino flavors over broad ranges of energy and luminosity in roughly the "bipolar" collective mode. We find that this large-scale flavor conversion, largely driven by the flavor off-diagonal neutrino-neutrino forward scattering potential, sets in much closer to the proto-neutron star than simple estimates based on flavor-diagonal potentials and Mikheyev-Smirnov-Wolfenstein evolution would indicate. In turn, this suggests that models of r -process nucleosynthesis sited in the neutrino-driven wind could be affected substantially by active-active neutrino flavor mixing, even with the small measured neutrino mass-squared differences.

We review the rich phenomena associated with neutrino flavor transformation in the presence of neutrino self-coupling. Our exposition centers on three collective neutrino oscillation scenarios: a simple bipolar neutrino system that initially consists of mono-energetic electron neutrinos and antineutrinos; a homogeneous and isotropic neutrino gas with multiple neutrino/antineutrino species and continuous energy spectra; and a generic neutrino gas in an anisotropic environment. We use each of these scenarios to illustrate key facets of collective neutrino oscillations. We discuss the implications of collective neutrino flavor oscillations for core collapse supernova physics and for the prospects of obtaining fundamental neutrino properties, e.g., the neutrino mass hierarchy and $\theta_{13}$ from a future observed supernova neutrino signal.Comment: Submitted to Annual Review of Nuclear and Particle Scienc

We examine coherent active-active channel neutrino flavor evolution in environments where neutrino-neutrino forward scattering can engender large-scale collective flavor transformation. We introduce the concept of neutrino flavor isospin which treats neutrinos and antineutrinos on an equal footing, and which facilitates the analysis of neutrino systems in terms of the spin precession analogy. We point out a key quantity, the "total effective energy", which is conserved in several important regimes. Using this concept, we analyze collective neutrino and antineutrino flavor oscillation in the "synchronized" mode and what we term the "bi-polar" mode. We thereby are able to explain why large collective flavor mixing can develop on short timescales even when vacuum mixing angles are small in, e.g., a dense gas of initially pure νe andνe with an inverted neutrino mass hierarchy (an example of bi-polar oscillation). In the context of the spin precession analogy, we find that the co-rotating frame provides insights into more general systems, where either the synchronized or bipolar mode could arise. For example, we use the co-rotating frame to demonstrate how large flavor mixing in the bi-polar mode can occur in the presence of a large and dominant matter background. We use the adiabatic condition to derive a simple criterion for determining whether the synchronized or bi-polar mode will occur. Based on this criterion we predict that neutrinos and antineutrinos emitted from a proto-neutron star in a core-collapse supernova event can experience synchronized and bi-polar flavor transformations in sequence before conventional Mikhyev-Smirnov-Wolfenstein flavor evolution takes over. This certainly will affect the analyses of future supernova neutrino signals, and might affect the treatment of shock re-heating rates and nucleosynthesis depending on the depth at which collective transformation arises.

We calculate coherent neutrino and antineutrino flavor transformation in the supernova environment, for the first time including self-consistent coupling of intersecting neutrino/antineutrino trajectories. For neutrino mass-squared difference |δm 2 | = 3 × 10 −3 eV 2 we find that in the normal (inverted) mass hierarchy the more tangentially-propagating (radially-propagating) neutrinos and antineutrinos can initiate collective, simultaneous medium-enhanced flavor conversion of these particles across broad ranges of energy and propagation direction. Accompanying alterations in neutrino/antineutrino energy spectra and fluxes could affect supernova nucleosynthesis and the expected neutrino signal.PACS numbers: 14.60. Pq, 97.60.Bw In this letter we present the first self-consistent solution to a long standing problem in following coherent flavor inter-conversion among neutrinos and antineutrinos in the region above the hot proto-neutron star subsequent to the supernova explosion [1]. The problem is that flavor histories on intersecting neutrino/antineutrino world lines can be coupled by neutral-current forward exchange scattering [2]. Many studies neglecting this aspect of flavor transformation [2,3,4,5,6,7,8,9,10] nevertheless have shown that flavor conversion in the neutrino and antineutrino fields above the proto-neutron star could be important in understanding the supernova explosion mechanism [3,4,5] and the origin of heavy r -process nuclei [2,6,7,8,9,10].Inelastic scattering processes and associated decoherence may dominate neutrino flavor development in the proto-neutron star core and in the region near the neutrino sphere, necessitating a full quantum kinetic approach there [11,12]. By contrast, in the hot bubble (a high-entropy region that develops above the neutrino sphere at time post-core-bounce t PB 3 s), where the r -process elements may be made, neutrinos and antineu- trinos for the most part propagate coherently. In this limit we can model the evolution of flavor along a single neutrino's trajectory with a mean field [13], Schrödinger-like equation, which in the effective 2 × 2 mixing channel isThe effective neutrino flavor evolution Hamiltonian can be expressed in the flavor basis aŝThe flavor evolution of an antineutrino is determined similarly but with A → −A, B → −B and B eτ → −B * eτ . In these expressions t is an Affine parameter along the neutrino's world line, ∆ ≡ δm 2 /2E ν , where E ν is neutrino energy, and δm 2 = m 2 3 − m 2 1 is the difference of the squares of the relevant vacuum neutrino mass eigenvalues. We focus on the atmospheric mass-squared difference δm 2 atm because it will give flavor transformation deeper in the supernova envelope than will the solar scale. Therefore, we set δm 2 = ±3 × 10 −3 eV 2 , where the plus (minus) sign is for the normal (inverted) mass hierarchy. In Eq. (2), θ is the effective 2 × 2 vacuum mixing angle. Flavor transformation in the ν e ⇋ ν µ,τ andν e ⇋ν µ,τ channels is most important in supernovae because there may be disparities in energy spectra a...

We study the flavor evolution of a dense gas initially consisting of pure mono-energetic νe andνe. Using adiabatic invariants and the special symmetry in such a system we are able to calculate the flavor evolution of the neutrino gas for the cases with slowly decreasing neutrino number densities. These calculations give new insights into the results of recent large-scale numerical simulations of neutrino flavor transformation in supernovae. For example, our calculations reveal the existence of what we term the "collective precession mode". Our analyses suggest that neutrinos which travel on intersecting trajectories subject to destructive quantum interference nevertheless can be in this mode. This mode can result in sharp transitions in the final energy-dependent neutrino survival probabilities across all trajectories, a feature seen in the numerical simulations. Moreover, this transition is qualitatively different for the normal and inverted neutrino mass hierarchies. Exploiting this difference, the neutrino signals from a future galactic supernova can potentially be used to determine the actual neutrino mass hierarchy.