Implications of nonzero ${\theta }_{13}$ for the neutrino mass hierarchy

Abstract

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 ${\nu }_{\mu }\to {\nu }_e$ 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 ${\theta }_{13}\to 0$ 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 NO$\nu$A, with different baselines and different matter effects, better able in combination to distinguish the hierarchy and the sign of ${\theta }_{13}$. The large value of ${\theta }_{13}$ yields effects from atmospheric data that distinguish hierarchies. We find for normal hierarchy, positive ${\theta }_{13}$, ${\sin }^{2}2{\theta }_{13}=0.090\pm 0.020$ and is 0.2% probable it is the correct combination; for normal hierarchy, negative ${\theta }_{13}$, ${\sin }^{2}2{\theta }_{13}=0.108\pm 0.023$ and is 2.2% probable; for inverse hierarchy, positive ${\theta }_{13}$, ${\sin }^{2}2{\theta }_{13}=0.110\pm 0.022$ and is 7.1% probable; for inverse hierarchy, negative ${\theta }_{13}$, ${\sin }^{2}2{\theta }_{13}=0.113\pm 0.022$ and is 90.5% probable, results that are inconsistent with two similar analyses.

8 pages, 8 figures, to appear in Horizons of Innovative Theories, Experiments, and Supercomputing in Nuclear Physics (New Orleans, June 4-6, 2012)

References in corpus (9)

• Observation of electron-antineutrino disappearance at Daya Bay
• Observation of Reactor Electron Antineutrino Disappearance in the RENO Experiment
• Indication of Electron Neutrino Appearance from an Accelerator-produced Off-axis Muon Neutrino Beam
• Indication for the disappearance of reactor electron antineutrinos in the Double Chooz experiment
• An improved measurement of muon antineutrino disappearance in MINOS
• Atmospheric, long baseline, and reactor neutrino data constraints on ${\theta }_{13}$
• On detecting CP violation in a single neutrino oscillation channel at very long baselines
• Calculating error bars for neutrino mixing parameters
• The impact of hierarchy upon the values of neutrino mixing parameters