Sterile Neutrinos: Propagation in Matter and Sensitivity to Sterile Mass Ordering

TL;DR

This paper derives analytical formulas for sterile neutrino effects in matter, enabling predictions of how sterile neutrino mass ordering influences long-baseline experiments like DUNE, especially for certain mass-squared differences.

Contribution

It provides exact analytical expressions for sterile neutrino oscillation probabilities in matter, including matter effects and dependence on sterile mass-squared differences, enhancing understanding of sterile neutrino signatures.

Findings

Sensitivity to sterile mass ordering can be significant at DUNE for |m^2_{41}|  10^{-4} to 10^{-2} eV^2.

Analytical formulas clarify the dependence of sterile neutrino effects on matter and m^2_{41}.

Resonance-like effects influence the sensitivity to sterile neutrino parameters.

Abstract

We analytically calculate the neutrino conversion probability $P_{\mu e}$ in the presence of sterile neutrinos, with exact dependence on $\Delta m^2_{41}$ and with matter effects explicitly included. Using perturbative expansion in small parameters, the terms involving the small mixing angles $\theta_{24}$ and $\theta_{34}$ can be separated out, with $\theta_{34}$ dependence only arising due to matter effects. We express $P_{\mu e}$ in terms of the quantities of the form $\sin(x)/x$, which helps in elucidating its dependence on matter effects and a wide range of $\Delta m^2_{41}$ values. Our analytic expressions allow us to predict the effects of the sign of $\Delta m^2_{41}$ at a long baseline experiment like DUNE. We numerically calculate the sensitivity of DUNE to the sterile mass ordering and find that this sensitivity can be significant in the range $|\Delta m^2_{41}| \sim (10^{-4} - 10^{-2})$ eV$^2$, for either mass ordering of active neutrinos. The dependence of this sensitivity on the value of $\Delta m^2_{41}$ for all mass ordering combinations can be explained by investigating the resonance-like terms appearing due to the interplay between the sterile sector and matter effects.