Symmetry, Hierarchy, and an Alternative Paradigm for Analyzing Neutrino Oscillations

Abstract

We conducted an updated global analysis of neutrino oscillation data using alternative bounds on the mixing angle theta-13 to determine the best fit mixing angles theta-13 and theta-23, the mass- squared difference ∆m_32^2, and the preferred neutrino mass hierarchy. Data analyzed included all the MINOS data, all the T2K data, Daya Bay, RENO, and the constraint from the Super- Kamiokande atmospheric data for the mixing angle theta-23. Using these alternative bounds highlights the presence of four solutions in the case of CP-conservation, one for each neutrino mass hierarchy and sign of theta-13 combination. The global data is sensitive enough to linear in theta-13 effects and symmetry-breaking matter effects in the long baseline accelerator data to distinguish between these four solutions. We find that the best fit solution is the normal hierarchy, positive theta-13 solution, which has a 58.6% probability of being the true solution. Using a full, exact, three- neutrino equation with a constant density matter profile and marginalizing over unwanted parameters, we find the best fit mixing parameters for this solution to be theta-13 = 0.158 - 0.012 + 0.014 rads, theta-23 = 0.868 -0.178 +0.039 rads, and ∆m_32^2 = 2.42 -0.08 +0.08 ~ 10^-3 eV^2.