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Multi-megaton scale under ice and underwater detectors of atmosphericneutrinos with few GeV's energy threshold (PINGU, ORCA) open up newpossibilities in the determination of neutrino properties, and in particularthe neutrino mass hierarchy. With a dense array of optical modules it will bepossible 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 substantiallyincrease with the measurement of $y$. It will enable (i) a partial separationof the neutrino and antineutrino signals; (ii) a better reconstruction of theneutrino direction; (iii) the reduction of the neutrino parameters degeneracy;(iv) a better control of systematic uncertainties; (v) a better identificationof the $\nu_\mu$ events. It will improve the sensitivity to the CP-violationphase. The three dimensional, $(E_\nu, \theta_\mu, y)$, $\nu_\mu-$oscillogramswith the kinematical as well as the experimental smearing are computed. Wepresent the asymmetry distributions in the $E_\nu - \theta_\mu$ plane fordifferent intervals of $y$ and study their properties. We show that theinelasticity information reduces the effect of degeneracy of parameters by 30%.With the inelasticity, the total significance of establishing mass hierarchymay increase by 20% - 50%, thus effectively increasing the volume of thedetector by factor 1.5 - 2.

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