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

Abstract

We analytically calculate the neutrino conversion probability $P_{\mu e}$ in the presence of sterile neutrinos, with exact dependence on $\Delta m_{41}^2$ 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 $\Delta m_{41}^2$ values. Our analytic expressions allow us to predict the effects of the sign of $\Delta m_{41}^2$ 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 $|\Delta m_{41}^2|\sim (10^{-4}-10^{-2})$ eV${}^2$, for either mass ordering of active neutrinos. The dependence of this sensitivity on the value of $\Delta m_{41}^2$ 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.

Comments: 25 pages, 5 figures