A compact analytical approximation for a light sterile neutrino oscillation in matter

TL;DR

This paper introduces a simplified analytical method for calculating neutrino oscillation probabilities involving light sterile neutrinos in matter, enhancing computational efficiency and accuracy for long baseline experiments.

Contribution

It develops a Jacobi-like diagonalization approach to derive accurate, simplified oscillation formulas for 3+1 neutrino mixing in constant matter density, improving upon existing methods.

Findings

Achieves high numerical accuracy with simplified formulas.

Enables fast computation suitable for long baseline experiments.

Provides analytical expressions that are easy to implement.

Abstract

The existence of light sterile neutrinos is a long standing question for particle physics. Several experimental ``anomalies'' could be explained by introducing ~eV mass scaled light sterile neutrinos. Many experiments are actively hunting for such light sterile neutrinos through neutrino oscillation. For long baseline experiments, matter effect needs to be treated carefully for precise neutrino oscillation probability calculation. However, it is usually time-consuming or analytical complexity. In this manuscript we adopt the Jacobi-like method to diagonalize the Hermitian Hamiltonian matrix and derive analytically simplified neutrino oscillation probabilities for 3 (active) + 1 (sterile)-neutrino mixing for a constant matter density. These approximations can reach quite high numerical accuracy while keeping its analytical simplicity and fast computing speed. It would be useful for the current and future long baseline neutrino oscillation experiments.