An illustration and analysis of the degeneracy in the search for the leptonic CP-violating angle and the neutrino mass hierarchy

Determination of the value of the leptonic CP-violating angle delta and the neutrino mass hierarchy sgn(dm^2_31) through long baseline neutrino oscillation experiments is systematically analyzed. We note that the two oscillation spectra are difficult to discriminate and lead to the degeneracy when they are peaked at the same energy and have the same peak probability. The condition of peak-matching is thereby introduced as a criterion of the presence of degeneracy. Matching of peaks is visualized as an intersection of trajectories traced by a peak of an oscillation spectrum while the value of delta is varied from 0 to 2pi. We numerically calculate a pair of trajectories for a pair of hierarchies and examine the degeneracy, especially the one on the hierarchy. We formulate the trajectory into analytic expressions and give an evaluation of the critical length, which is shown to be proportional to 1/sin(theta_13). We take the following four approaches to solving the hierarchy degeneracy and provide prospects in view of our analysis: elongating the baseline length sufficiently, using both neutrinos and anti-neutrinos, combining experiments with different baseline lengths, and observing two or more oscillation peaks