New Paradigm for the Analysis of Three Neutrino Oscillation Data: Hierarchy

A new approach to the analysis of neutrino oscillation data, with CP = 0, is proposed. A four fold symmetry exists for vacuum oscillations with $\theta_{13} = 0$. For $\theta_{13}\ne 0$, the four fold symmetry breaks into two two-fold symmetries given by the change in hierarchy and a change in the sign of $\theta_{13}$. Matter effects break this symmetry. We perform a global data analysis that maintains the four independent solutions. We find the oscillation probability $\mathcal{P}_{\mu\mu}$ breaks the symmetry at a level that is not insignificant. The largest symmetry breaking arises from $\mathcal{P}_{\mu e}$. The mixing parameters for each of the four solutions are quite similar to those found by others for positive $\theta_{13}$, the case studied by them. The best fit solution is for the normal hierarchy, positive $\theta_{13}$ case with a probability of 58.6\% that it is the correct result of the four possible cases. The second best fit is inverse hierarchy and negative $\theta_{13}$, the symmetry partner of the best fit, with a probability of 27.9\%. The probability that $\theta_{13}$ is positive is found to be 64.9\%, and the probability that normal hierarchy is correct is 65.8\%. Preliminary CP-violating results will be presented.