Neutrino Flavor Pendulum Reloaded: The Case of Fast Pairwise Conversion

TL;DR

This paper presents a novel analogy between neutrino flavor conversion in supernovae and a gyroscopic pendulum, enabling prediction of flavor transformation depth through linear analysis without solving complex nonlinear equations.

Contribution

The study introduces the concept of the 'pendulum spin' as a key factor in determining flavor conversion depth, linking linear eigenfrequency analysis to nonlinear neutrino behavior.

Findings

Identifies the 'pendulum spin' as a crucial factor in flavor conversion.

Establishes a formal equivalence between neutrino oscillations and a gyroscopic pendulum.

Provides a diagnostic tool to predict flavor transformation without solving nonlinear equations.

Abstract

In core-collapse supernovae or compact binary merger remnants, neutrino-neutrino refraction can spawn fast pair conversion of the type $\nu_e \bar\nu_e \leftrightarrow \nu_x \bar\nu_x$ (with $x=\mu, \tau$), governed by the angle-dependent density matrices of flavor lepton number. In a homogeneous and axially symmetric two-flavor system, all angle modes evolve coherently, and we show that the nonlinear equations of motion are formally equivalent to those of a gyroscopic pendulum. Within this analogy, our main innovation is to identify the elusive characteristic of the lepton-number angle distribution that determines the depth of conversion with the "pendulum spin." The latter is given by the real part of the eigenfrequency resulting from the linear normal-mode analysis of the neutrino system. This simple analogy allows one to predict the depth of flavor conversion without solving the nonlinear evolution equations. Our approach provides a novel diagnostic tool to explore the physics of nonlinear systems.