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

Abstract

Determination of the value of the leptonic CP-violating phase deltaand the neutrino mass hierarchy sgn(dm2_31) through long baselineneutrino oscillation experiments is systematically analyzed. We notethat the two oscillation spectra are difficult to discriminate andlead to the degeneracy when they are peaked at the same energy andhave the same peak probability. The condition of peak-matching istherefore introduced as a criterion for the presence of degeneracy.The matching of peaks is visualized as an intersection of trajectoriestraced by the peak of an oscillation spectrum while the value of deltais varied from 0 to 2pi. We numerically calculate a pair oftrajectories for a pair of hierarchies and examine the degeneracy,especially that concerning the hierarchy. We formulate the trajectoryin terms of analytic expressions and evaluate the critical length,which is shown to be proportional to 1/sin(theta_13). In view of ouranalysis, we discuss future prospects to solve the hierarchydegeneracy with regard to the following four approaches: elongatingthe baseline length sufficiently, using both neutrinos andanti-neutrinos, combining experiments with different baseline lengths,and observing two or more oscillation peaks.