Implications Of Nonzero Theta(13) For The Neutrino Mass Hierarchy

The Daya Bay, RENO, and Double Chooz experiments have discovered a large non-zero value for theta(13). We present a global analysis that includes these three experiments, Chooz, the Super-K atmospheric data, and the v(mu) -> v(e) T2K and MINOS experiments that are sensitive to the hierarchy and the sign of theta(13). We report preliminary results in which we fix the mixing parameters other than theta(13) to those from a recent global analysis. Given there is no evidence for a non-zero CP violation, we assume delta = 0. T2K and MINOS lie in a region of L/E where there is a hierarchy degeneracy in the limit of theta(13) -> 0 and no matter interaction. For non-zero theta(13), the symmetry is partially broken, but a degeneracy under the simultaneous exchange of both hierarchy and the sign of theta(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 NOvA, with different baselines and different matter effects, better able in combination to distinguish the hierarchy and the sign of theta(13). The present T2K and MINOS data do not distinguish between hierarchies or the sign of theta(13), but the large value of theta(13) yields effects from atmospheric data that do. We find for normal hierarchy, positive theta(13), sin(2) 2 theta(13) = 0.090 +/- 0.020 and is 0.2% probable it is the correct combination; for normal hierarchy, negative theta(13), sin(2) 2 theta(13) = 0.108 +/- 0.023 and is 2.2% probable; for inverse hierarchy, positive theta(13), sin(2) 2 theta(13) = 0.110 +/- 0.022 and is 7.1% probable; for inverse hierarchy, negative theta(13), sin(2) 2 theta(13) = 0.113 +/- 0.022 and is 90.5% probable, results that are inconsistent with two similar analyses.