Fast Neutrino Flavor Conversion as Oscillations in a Quartic Potential

TL;DR

This paper provides an analytical framework for understanding fast neutrino flavor conversions in dense environments, modeling the process as a particle rolling in a quartic potential, advancing beyond previous linear and numerical studies.

Contribution

It introduces an analytical approach to describe fast neutrino flavor conversions, interpreting the phenomenon as a particle in a quartic potential, which was previously understood mainly through linear analysis and simulations.

Findings

Conversion dynamics resemble a particle rolling in a quartic potential.

Fast conversions can be analytically described beyond linear approximations.

Seeding of fast conversions involves slower oscillations.

Abstract

Neutrinos in dense environments undergo collective pair conversions $\nu_e\bar{\nu}_e \leftrightarrow \nu_x\bar{\nu}_x$, where $x$ is a non-electron flavor, due to forward scattering off each other that may be a crucial ingredient for supernova explosions. Depending on the flavor-dependent local angular distributions of the neutrino fluxes, the conversion rate can be "fast", i.e., of the order $\mu=\sqrt{2}G_F n_\nu$, which can far exceed the usual neutrino oscillation frequency $\omega=\Delta m^2/(2E)$. Until now, this surprising nonlinear phenomenon has only been understood in the linear regime and explored further using numerical experiments. We present an analytical treatment of the simplest system that exhibits fast conversions, and show that the conversion can be understood as the dynamics of a particle rolling down in a quartic potential governed dominantly by $\mu$, but seeded by slower oscillations.