Fourier Analysis of the Parametric Resonance in Neutrino Oscillations

TL;DR

This paper uses Fourier analysis to understand how inhomogeneous matter affects neutrino oscillation probabilities, revealing resonance conditions and the impact of different Fourier modes on the energy spectrum.

Contribution

It introduces a Fourier-based approach to analyze parametric resonance in neutrino oscillations, providing analytic solutions and insights into the effects of matter density variations.

Findings

Fourier modes modify the energy spectrum at corresponding energies.

Large-scale variations affect high-energy oscillations, small-scale variations affect low-energy ones.

The enhancement manifests as a slow oscillation, confirmed by numerical analysis.

Abstract

Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to the simple parametric resonance, the enhancement of the oscillation probability is itself an slow oscillation as demonstrated by a numerical analysis with a single Fourier mode of the matter density. We derive an analytic solution to the evolution equation on the resonance energy, including the expression of frequency of the slow oscillation.