Stepwise Spectral Swapping with Three Neutrino Flavors

TL;DR

This paper introduces a framework for analyzing collective three-flavor neutrino oscillations, demonstrating how spectral swaps emerge and are affected by matter backgrounds, with implications for understanding neutrino flavor evolution in astrophysical environments.

Contribution

It extends two-flavor oscillation techniques to three flavors, showing how spectral swaps naturally arise and are influenced by matter effects and mixing parameters.

Findings

Spectral swaps can be explained by an adiabatic/precession solution.

Two stepwise spectral swaps appear naturally in the three-flavor scenario.

Spectral swap behavior is sensitive to deviations from maximal 23-mixing.

Abstract

We develop a framework for studying collective three-flavor neutrino oscillations based on the density matrix formalism. We show how techniques proven useful for collective two-flavor neutrino oscillations such as corotating frames can be applied readily to three-flavor mixing. Applying two simple assumptions and the conservation of two ``lepton numbers'' we use this framework to demonstrate how the adiabatic/precession solution emerges. We illustrate with a numerical example how two stepwise spectral swaps appear naturally if the flavor evolution of the neutrino gas can be described by such a solution. For the special case where mu and tau flavor neutrinos are equally mixed and are produced with identical energy spectra and total numbers, we find that one of the spectral swaps in the three-flavor scenario agrees with that in the two-flavor scenario when appropriate mixing parameters are used. Using the corotating frame technique we show how the adiabatic/precession solution can obtain even in the presence of a dominant ordinary matter background. With this solution we can explain why neutrino spectral swapping can be sensitive to deviations from maximal 23-mixing when the ``mu-tau'' matter term is significant.