Implications of nonzero θ13 for the neutrino mass hierarchy

The Daya Bay, RENO, and Double Chooz experiments have discovered a large non-zero value for θ13. We present a global analysis that includes these three experiments, Chooz, the Super-K atmospheric data, and the νμ → νe T2K and MINOS experiments that are sensitive to the hierarchy and the sign of θ13. We report preliminary results in which we fix the mixing parameters other than θ13 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 θ13 → 0 and no matter interaction. For nonzero θ13, the symmetry is partially broken, but a degeneracy under the simultaneous exchange of both hierarchy and the sign of θ13 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 NOνA, with different baselines and different matter effects, better able in combination to distinguish the hierarchy and the sign of θ13. The present T2K and MINOS data do not distinguish between hierarchies or the sign of θ13, but the large value of θ13 yields effects from atmospheric data that do. We find for normal hierarchy, positive θ13, sin 2 2θ13 = 0.090± 0.020 and is 0.2% probable it is the correct combination; for normal hierarchy, negative θ13, sin 2 2θ13 = 0.108 ± 0.023 and is 2.2% probable; for inverse hierarchy, positive θ13, sin 2 2θ13 = 0.110±0.022 and is 7.1% probable; for inverse hierarchy, negative θ13, sin 2 2θ13 = 0.113± 0.022 and is 90.5% probable, results that are inconsistent with two similar analyses.