Invariants of Collective Neutrino Oscillations

We consider the flavor evolution of a dense neutrino gas by taking into account both vacuum oscillations and self interactions of neutrinos. We examine the system from a many-body perspective as well as from the point of view of an effective one-body description formulated in terms of the neutrino polarization vectors. We show that, in the single angle approximation, both the many-body picture and the effective one-particle picture possess several constants of motion. We write down these constants of motion explicitly in terms of the neutrino isospin operators for the many-body case and in terms of the polarization vectors for the effective one-body case. The existence of these constants of motion is a direct consequence of the fact that the collective neutrino oscillation Hamiltonian belongs to the class of Gaudin Hamiltonians. This class of Hamiltonians also includes the (reduced) BCS pairing Hamiltonian describing superconductivity. We point out the similarity between the collective neutrino oscillation Hamiltonian and the BCS pairing Hamiltonian. The constants of motion manifest the exact solvability of the system. Borrowing the well established techniques of calculating the exact BCS spectrum, we present exact eigenstates and eigenvalues of both the many-body and the effective one-particle Hamiltonians describing the collective neutrino oscillations. For the effective one-body case, we show that spectral splits of neutrinos can be understood in terms of the adiabatic evolution of some quasi-particle degrees of freedom from a high density region where they coincide with flavor eigenstates to the vacuum where they coincide with mass eigenstates. We write down the most general consistency equations which should be satisfied by the effective one-body eigenstates and show that they reduce to the spectral split consistency equations for the appropriate initial conditions.Comment: 26 pages with one figure. Published versio

A Simultaneous Solution to the ^6Li and ^7Li Big Bang Nucleosynthesis Problems from a Long-Lived Negatively-Charged Leptonic Particle

The $^6$Li abundance observed in metal poor halo stars exhibits a plateau similar to that for $^7$Li suggesting a primordial origin. However, the observed abundance of $^6$Li is a factor of $10^3$ larger and that of $^7$Li is a factor of 3 lower than the abundances predicted in the standard big bang when the baryon-to-photon ratio is fixed by WMAP. Here we show that both of these abundance anomalies can be explained by the existence of a long-lived massive, negatively-charged leptonic particle during nucleosynthesis. Such particles would capture onto the synthesized nuclei thereby reducing the reaction Coulomb barriers and opening new transfer reaction possibilities, and catalyzing a second round of big bang nucleosynthesis. This novel solution to both of the Li problems can be achieved with or without the additional effects of stellar destruction.Comment: 6 pages, 2 figures, to be published in Physical Review