Neutrino flavor pendulum in both mass hierarchies

Understand

We construct a simple example for self-induced flavor conversion in dense neutrino gases showing new solutions that violate the symmetries of initial conditions.

• Our system consists of two opposite momentum modes 1 and 2, each initially occupied with equal densities of nu_e and anti-nu_e.
• Restricting solutions to symmetry under 1 <-> 2 allows for the usual bimodal instability (&#34;flavor pendulum&#34;) in the inverted neutrino mass hierarchy (IH) and stability (no self-induced flavor conversion) in the normal hierarchy (NH).
• Lifting this symmetry restriction allows for a second pendulum-like solution that occurs in NH where the modes 1 and 2 swing in opposite directions in flavor space.