Matter Effect of Light Sterile Neutrino: An Exact Analytical Approach

TL;DR

This paper derives exact analytical formulas for active neutrino oscillation probabilities in terrestrial matter, including sterile neutrino effects, revealing significant contributions in certain parameter spaces and emphasizing the role of Dirac phases.

Contribution

It provides the first exact analytical expressions for neutrino oscillations with sterile neutrinos in matter, facilitating precise analysis of experimental data.

Findings

Sterile neutrinos significantly affect matter oscillation probabilities in certain parameters.

Dirac CP-violating phases are crucial in sterile neutrino contributions.

Formulas can be adapted for various medium and long baseline experiments.

Abstract

The light sterile neutrino, if it exists, will give additional contribution to matter effect when active neutrinos propagate through terrestrial matter. In the simplest 3+1 scheme, three more rotation angles and two more CP-violating phases in lepton mixing matrix make the interaction complicated formally. In this work, the exact analytical expressions for active neutrino oscillation probabilities in terrestrial matter, including sterile neutrino contribution, are derived. It is pointed out that this set of formulas contain information both in matter and in vacuum, and can be easily tuned by choosing related parameters. Based on the generic exact formulas, we present oscillation probabilities of typic medium and long baseline experiments. Taking NO$\nu$A experiment as an example, we show that in particular parameter space sterile neutrino gives important contribution to terrestrial matter effect, and Dirac phases play a vital role.