Sterile Neutrinos: Propagation in Matter and Mass Ordering

We analytically calculate the 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, we show that the terms involving mixing angles \(\theta _{24}\) and \(\theta _{34}\) can be separated out, with the effects of the latter only arising due to neutral current forward scattering of active neutrinos. Moreover, the conversion probability \(P_{\mu e}\) can be rearranged as a summation of terms of the form \(\sin (x)/x\) , which helps in the physical understanding of where the effects of different possible values of \(\Delta m^2_{41}\) dominate. We further focus on the identification of sterile mass ordering at a long baseline experiment like DUNE. Our analytic expressions allow us to predict how the effects of sign of \(\Delta m^2_{41}\) would manifest, for both possible signs of \(\Delta m^2_{31}\) . We numerically calculate the sensitivity of DUNE to sterile mass ordering over a large range of \(\Delta m^2_{41}\) and explain the features of this sensitivity using our analytic expressions.