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Results from experiments like LSND and MiniBooNE hint towards the possiblepresence of an extra eV scale sterile neutrino. The addition of such a neutrinowill significantly impact the standard three flavour neutrino oscillations. Inparticular, it can give rise to additional degeneracies due to additionalsterile parameters. For an eV scale sterile neutrino, the cosmologicalconstraints dictate that the sterile state is heavier than the three activestates. However, for lower masses of sterile neutrinos, it can be lighter thanone and/or more of the three states. In such cases, the mass ordering of thesterile neutrinos also becomes unknown along with the mass ordering of theactive states. In this paper, we explore the mass ordering sensitivity in thepresence of a sterile neutrino assuming the mass squared difference$|\Delta_{41}|$ to be in the range $10^{-4} - 1$ eV$^2$. We study (i) how theordering of the active states, i.e. the determination of the sign of$\Delta_{31}$ gets affected by the presence of a sterile neutrino in the abovemass range, (ii) the possible determination of the sign of $\Delta_{41}$ for$\Delta_{41}$ in the range $10^{-4} - 0.1$ eV$^2$. This analysis is done in thecontext of a liquid argon detector using both beam neutrinos traveling adistance of 1300 km and atmospheric neutrinos which propagates through adistance ranging from 10 - 10000 km allowing resonant matter effects. Apartfrom presenting separate results from these sources, we also do a combinedstudy and probe the synergy between these two in giving an enhancedsensitivity.

Probing mass orderings in presence of a very light sterile neutrino in a liquid argon detector