Neutrino conversion in a neutrino flux: Towards an effective theory of collective oscillations

TL;DR

This paper develops an effective linear theory for collective neutrino oscillations in supernovae, analyzing conditions for strong flavor transformations and the impact of flux properties on these phenomena.

Contribution

It introduces an effective theory based on external potentials and explores parametric resonance effects in neutrino flavor conversions.

Findings

Strong flavor transformations can be interpreted as parametric resonance effects.

Integrations over energies and emission points suppress flavor transformations.

Changes in background densities also suppress collective oscillations.

Abstract

Collective oscillations of supernova neutrinos above the neutrino sphere can be completely described by the propagation of individual neutrinos in external potentials and are in this sense a linear phenomenon. An effective theory of collective oscillations can be developed based on certain assumptions about time dependence of these potentials. General conditions for strong flavor transformations are formulated and these transformations can be interpreted as parametric resonance effects induced by periodic modulations of the potentials. We study a simplified and solvable example, where a probe neutrino is propagating in a flux of collinear neutrinos, such that $\nu \nu-$ interactions in the flux are absent. Still, this example retains the main feature - the coherent flavor exchange. Properties of the parametric resonance are studied, and it is shown that integrations over energies and emission points of the flux neutrinos suppress modulations of the potentials and therefore strong transformations. The transformations are also suppressed by changes in densities of background neutrinos and electrons.