Fourier Analysis of the Parametric Resonance of the Neutrino Oscillation in the Presence of Inhomogeneous Matter

TL;DR

This paper uses Fourier analysis to investigate how spatial variations in matter density influence neutrino oscillation resonance conditions, clarifying the relationship between matter profile frequencies and oscillation behavior.

Contribution

It introduces a Fourier-based framework to analyze parametric resonance in neutrino oscillations caused by inhomogeneous matter density profiles.

Findings

Resonance occurs when oscillation frequency matches matter density variation frequency.

Fourier modes of matter density affect the energy spectrum at specific dips.

The analysis clarifies the resonance condition in inhomogeneous environments.

Abstract

We study the parametric resonance of the neutrino oscillation through the matter whose density varies spatially. The Fourier analysis of the matter effect enables us to clarify the parametric resonance condition, which is summarized in a frequency matching between the neutrino oscillation and the spatial variation of the matter density. As a result, the n-th Fourier mode of a matter density profile modifies the energy spectrum of the nu_mu -> nu_e appearance probability at around the n-th dip.