Neutrino Magnetic Moment, CP Violation and Flavor Oscillations in Matter

TL;DR

This paper explores the complex nonlinear flavor oscillations of neutrinos in dense astrophysical environments, analyzing symmetries, CP violation, and magnetic moments within a comprehensive three-flavor framework.

Contribution

It extends the understanding of neutrino collective oscillations by identifying symmetries and constants of motion in a full three-flavor, many-body context, including effects of CP violation and magnetic moments.

Findings

Dynamical symmetries exist in three-flavor neutrino oscillations under certain conditions.

CP violation effects can be decoupled from the many-body evolution in the absence of magnetic interactions.

Neutrino magnetic moments influence flavor evolution, especially in strong magnetic fields.

Abstract

We consider collective oscillations of neutrinos, which are emergent nonlinear flavor evolution phenomena instigated by neutrino-neutrino interactions in astrophysical environments with sufficiently high neutrino densities. We investigate the symmetries of the problem in the full three flavor mixing scheme and in the exact many-body formulation by including the effects of CP violation and neutrino magnetic moment. We show that, similar to the two flavor scheme, several dynamical symmetries exist for three flavors in the single-angle approximation if the net electron background in the environment and the effects of the neutrino magnetic moment are negligible. Moreover, we show that these dynamical symmetries are present even when the CP symmetry is violated in neutrino oscillations. We explicitly write down the constants of motion through which these dynamical symmetries manifest themselves in terms of the generators of the SU(3) flavor transformations. We also show that the effects due to the CP-violating Dirac phase factor out of the many-body evolution operator and evolve independently of nonlinear flavor transformations if neutrino electromagnetic interactions are ignored. In the presence of a strong magnetic field, CP-violating effects can still be considered independently provided that an effective definition for neutrino magnetic moment is used.