Improving the neutrino mass hierarchy identification with inelasticity measurement in PINGU and ORCA

Multi-megaton scale under ice and underwater detectors of atmospheric neutrinos with few GeV's energy threshold (PINGU, ORCA) open up new possibilities in the determination of neutrino properties, and in particular the neutrino mass hierarchy. With a dense array of optical modules it will be possible to determine the inelasticity, $y$, of the charged current $\nu_\mu$ events in addition to the neutrino energy $E_\nu$ and the muon zenith angle $\theta_\mu$. The discovery potential of the detectors will substantially increase with the measurement of $y$. It will enable (i) a partial separation of the neutrino and antineutrino signals; (ii) a better reconstruction of the neutrino direction; (iii) the reduction of the neutrino parameters degeneracy; (iv) a better control of systematic uncertainties; (v) a better identification of the $\nu_\mu$ events. It will improve the sensitivity to the CP-violation phase. The three dimensional, $(E_\nu, \theta_\mu, y)$, $\nu_\mu-$oscillograms with the kinematical as well as the experimental smearing are computed. We present the asymmetry distributions in the $E_\nu - \theta_\mu$ plane for different intervals of $y$ and study their properties. We show that the inelasticity information reduces the effect of degeneracy of parameters by 30%. With the inelasticity, the total significance of establishing mass hierarchy may increase by 20% - 50%, thus effectively increasing the volume of the detector by factor 1.5 - 2.