We explore the potential offered by large-mass liquid argon detectors for determination of the sign of $\Delta m_{31}^2$, or the neutrino mass hierarchy, through interactions of atmospheric neutrinos. We give results for a 100 kT sized magnetized detector which provides separate sensitivity to ${\nu }_{\mu }$, ${\overline{\nu }}_{\mu }$ and, over a limited energy range, to ${\nu }_e$, ${\overline{\nu }}_e$. We also discuss the sensitivity for the unmagnetized version of such a detector. After including the effect of smearing in neutrino energy and direction and incorporating the relevant statistical, theoretical, and systematic errors, we perform a binned ${\chi }^2$ analysis of simulated data. The ${\chi }^2$ is marginalized over the presently allowed ranges of neutrino parameters and determined as a function of ${\theta }_{13}$. We find that such a detector offers superior capabilities for hierarchy resolution, allowing a $>4\sigma$ determination for a 100 kT detector over a 10-year running period for values of ${sin}^{2}2{\theta }_{13}\ge 0.05$. For an unmagnetized detector, a $2.5\sigma$ hierarchy sensitivity is possible for ${sin}^{2}2{\theta }_{13}=0.04$.

• Received 7 August 2008

DOI:https://doi.org/10.1103/PhysRevD.78.073001