An Illustration and Analysis of the Degeneracy in the Search for the Leptonic CP-Violating Phase and the Neutrino Mass Hierarchy

Determination of the value of the leptonic CP-violating phase deltaand theneutrino mass hierarchy sgn(dm2_31) through long baselineneutrino oscillationexperiments is systematically analyzed. We notethat the two oscillation spectraare difficult to discriminate andlead to the degeneracy when they are peaked atthe same energy andhave the same peak probability. The condition ofpeak-matching istherefore introduced as a criterion for the presence ofdegeneracy.The matching of peaks is visualized as an intersection oftrajectoriestraced by the peak of an oscillation spectrum while the value ofdeltais varied from 0 to 2pi. We numerically calculate a pair oftrajectoriesfor a pair of hierarchies and examine the degeneracy,especially that concerningthe hierarchy. We formulate the trajectoryin terms of analytic expressions andevaluate the critical length,which is shown to be proportional to1/sin(theta_13). In view of ouranalysis, we discuss future prospects to solvethe hierarchydegeneracy with regard to the following four approaches:elongatingthe baseline length sufficiently, using both neutrinosandanti-neutrinos, combining experiments with different baseline lengths,andobserving two or more oscillation peaks.Comment: PTPTeX, 23 pages, 11 figures. Minor updates in accordance with the published versio