Neutrino oscillations with three flavors in matter: Applications to neutrinos traversing the Earth

TL;DR

This paper derives analytic formulas for three-flavor neutrino oscillations in matter, enabling precise calculations of transition probabilities relevant for atmospheric and long baseline neutrino experiments traversing Earth's varying density.

Contribution

It provides new analytic expressions for neutrino oscillations in matter, including the time evolution operator and transition probabilities, applicable to realistic Earth density profiles.

Findings

Derived explicit formulas for three-flavor neutrino oscillations in matter.

Applied formulas to Earth's mantle-core-mantle density profile.

Facilitated accurate predictions for atmospheric and long baseline neutrino experiments.

Abstract

Analytic formulas are presented for three flavor neutrino oscillations in matter in the plane wave approximation. We calculate in particular the time evolution operator in both mass and flavor bases. We also find the transition probabilities expressed as functions of the vacuum mass squared differences, the vacuum mixing angles, and the matter density parameter. The application of this to neutrino oscillations for both atmospheric and long baseline neutrinos in a mantle-core-mantle step function model of the Earth's matter density profile is discussed.