Collective neutrino flavor transitions in supernovae and the role of trajectory averaging

Non-linear effects on supernova neutrino oscillations, associated with neutrino-neutrino interactions, are known to induce collective flavor transformations near the supernova core for theta(13) not equal 0. In scenarios with very shallow electron density profiles, these transformations have been shown to couple with ordinary matter effects, jointly producing spectral distortions both in normal and in inverted hierarchy. In this work we consider a complementary scenario, characterized by higher electron density, as indicated by shock-wave simulations during a few seconds after bounce. In this case, early collective flavor transitions are decoupled from later, ordinary matter effects. Moreover, such transitions become more amenable to both numerical computations and analytical interpretations in inverted hierarchy, while they basically vanish in normal hierarchy. We numerically evolve the neutrino density matrix in the region relevant for self-interaction effects, using thermal spectra and a representative value sin(2)theta(13) = 10(-4). In the approximation of averaged intersection angle between neutrino trajectories, our simulations neatly show the collective phenomena of synchronization, bipolar oscillations, and spectral split, with analytically understandable features, as recently discussed in the literature. In the more realistic (but computationally demanding) case of non-averaged neutrino trajectories, our simulations do not show new significant qualitative features, apart from the smearing of 'fine structures' such as bipolar nutations. Our results seem to suggest that, at least for non-shallow matter density profiles, averaging over neutrino trajectories plays a minor role in the final outcome. In this case, the swap of nu(e) and nu(mu,tau) spectra above a critical energy may represent an unmistakable signature of the inverted neutrino hierarchy, especially for theta(13) small enough to render further (ordinary or even turbulent) matter effects irrelevant.