Peak loops untying the degeneracy of the neutrino parameters

Systematic analysis of the determination of the value of leptonic CP-violating angle δ and the neutrino mass hierarchy sgnδm₃₁² by long baseline neutrino oscillation experiments is presented. We note the difficulty to distinguish a pair of oscillation probability spectra that are peaked at the same energy and have the same probability at that energy. We thereby set forth the peak-matching condition as a criterion of the presence of degeneracy, and visualize it by intersections of the trajectories drawn by a peak of an oscillation spectrum while the value of δ is varied from 0 to 2π. We numerically calculate the pairs of the trajectories for both hierarchies and show that the pair becomes disjoint as the baseline gets longer than a critical length, indicating the matter effect resolving the degeneracy on the hierarchy. We formulate the trajectories into analytic expressions and evaluate the critical length. We provide prospects of the following four approaches of resolving the hierarchy: making the baseline longer than the critical length, using both neutrinos and anti-neutrinos, combining experiments with different baseline lengths, and observing two or more oscillation peaks. (author)