Hierarchy independent sensitivity to leptonic $\delta_{CP}$ with low energy atmospheric neutrinos

One of the important unknowns in neutrino oscillation physics is the leptonic CP phase $\delta_{CP}$. Because of the ambiguity between $\delta_{CP}$ and neutrino mass hierarchy, experiments have to be designed in such a way as to measure these parameters independent of each other. Long baseline experiments like DUNE is exclusively designed to measure $\delta_{CP}$ in regions without hierarchy ambiguity and atmospheric neutrino experiments like INO are designed to measure hierarchy without $\delta_{CP}$ ambiguity. However atmospheric neutrinos are not usually used to probe $\delta_{CP}$. Here we present that, sub--GeV energy atmospheric neutrinos can be used to probe $\delta_{CP}$ irrespective of mass hierarchy. We show that when the events are binned as a function of $(E^{\rm{obs}}_l,\cos\theta^{\rm{obs}}_l)$, the observed energy and direction of the final state leptons in charged current interactions of $\nu$ and $\overline{\nu}$, a consistent distinction between various $\delta_{CP}$ values is obtained. Since there is no sensitivity to the mass ordering/hierarchy, $\delta_{CP}$ can be measured without hierarchy ambiguity at these energies. Sensitivity studies with ideal as well as realistic cases are discussed.