Parametric Resonance in Neutrino Oscillation: A Guide to Control the Effects of Inhomogeneous Matter Density

TL;DR

This paper explores how inhomogeneous matter density affects neutrino oscillations, demonstrating that Fourier mode analysis can control and predict these effects through parametric resonance, aiding precise oscillation probability calculations.

Contribution

It introduces a Fourier-based approach to analyze and control matter density effects on neutrino oscillations, highlighting the role of parametric resonance for systematic uncertainty management.

Findings

Each Fourier mode has a target energy affecting oscillation probability.

High Fourier modes influence low-energy neutrino oscillations.

Fourier analysis provides guidelines for controlling matter density uncertainties.

Abstract

Effects of the inhomogeneous matter density on the three-generation neutrino oscillation probability are analyzed. Realistic profile of the matter density is expanded into a Fourier series. Taking in the Fourier modes one by one, we demonstrate that each mode has its corresponding target energy. The high Fourier mode selectively modifies the oscillation probability of the low-energy region. This rule is well described by the parametric resonance between the neutrino oscillation and the matter effect. The Fourier analysis gives a simple guideline to systematically control the uncertainty of the oscillation probability caused by the uncertain density of matter. Precise analysis of the oscillation probability down to the low-energy region requires accurate evaluation of the Fourier coefficients of the matter density up to the corresponding high modes.