Implications of nonzero $θ_{13}$ for the neutrino mass hierarchy

The Daya Bay, RENO, and Double Chooz experiments have discovered a large non-zero value for $θ_{13}$. We present a global analysis that includes these three experiments, Chooz, the Super-K atmospheric data, and the $ν_μ\rightarrow ν_e$ T2K and MINOS experiments that are sensitive to the hierarchy and the sign of $θ_{13}$. We report preliminary results in which we fix the mixing parameters other than $θ_{13}$ to those from a recent global analysis. Given there is no evidence for a non-zero CP violation, we assume $δ=0$. T2K and MINOS lie in a region of $L/E$ where there is a hierarchy degeneracy in the limit of $θ_{13}\rightarrow 0$ and no matter interaction. For non-zero $θ_{13}$, the symmetry is partially broken, but a degeneracy under the simultaneous exchange of both hierarchy and the sign of $θ_{13}$ remains. Matter effects break this symmetry such that the positions of the peaks in the oscillation probabilities maintain the two-fold symmetry, while the magnitude of the oscillations is sensitive to the hierarchy. This renders T2K and NO$ν$A, with different baselines and different matter effects, better able in combination to distinguish the hierarchy and the sign of $θ_{13}$. The large value of $θ_{13}$ yields effects from atmospheric data that distinguish hierarchies. We find for normal hierarchy, positive $θ_{13}$, $\sin^22θ_{13}=0.090\pm0.020$ and is 0.2% probable it is the correct combination; for normal hierarchy, negative $θ_{13}$, $\sin^22θ_{13}=0.108\pm0.023$ and is 2.2% probable; for inverse hierarchy, positive $θ_{13}$, $\sin^22θ_{13}=0.110\pm0.022$ and is 7.1% probable; for inverse hierarchy, negative $θ_{13}$, $\sin^22θ_{13}=0.113\pm0.022$ and is 90.5% probable, results that are inconsistent with two similar analyses.

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