Three Neutrino Oscillations in Matter

TL;DR

This paper analytically solves the three-neutrino oscillation problem in constant matter density, providing explicit formulas for oscillation probabilities with modified mixing angles and mass eigenvalues.

Contribution

It introduces a method to derive simple, explicit formulas for three-neutrino oscillations in matter, extending previous approaches to include matter effects.

Findings

Analytical expressions for oscillation probabilities in matter

Explicit modifications of mixing angles and mass eigenvalues

Simplified parametric form similar to vacuum oscillations

Abstract

Following similar approaches in the past, the Schrodinger equation for three neutrino propagation in matter of constant density is solved analytically by two successive diagonalizations of 2x2 matrices. The final result for the oscillation probabilities is obtained directly in the conventional parametric form as in the vacuum but with explicit simple modification of two mixing angles ($\theta_{12}$ and $\theta_{13}$) and mass eigenvalues.