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

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 034 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)| similar to(10(-4) - 10(-2)) eV(2), for either mass ordering of active neutrinos. The dependence of this sensitivity on the value of delta m(241) 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.