Sterile neutrinos: propagation in matter and sensitivity to sterile mass ordering

A bstract We analytically calculate the neutrino conversion probability P μe in the presence of sterile neutrinos, with exact dependence on ∆ m 41 2 and with matter effects explicitly included. Using perturbative expansion in small parameters, the terms involving the small mixing angles θ 24 and θ 34 can be separated out, with θ 34 dependence only arising due to matter effects. We express P μe 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 ∆ m 41 2 values. Our analytic expressions allow us to predict the effects of the sign of ∆ 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 ∣ Δ m 41 2 ∣ ∼ 10 − 4 − 10 − 2 eV 2 , for either mass ordering of active neutrinos. The dependence of this sensitivity on the value of ∆ 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.