Neutrino mass hierarchy and δ^CP investigation within the biprobability (P-P^T) plane

This article illustrates the possibility of investigating the mass hierarchy and CP-violating phase δ^CP in the context of CP trajectory diagrams in the biprobability plane. The separation between the normal mass hierarchy (NH) and inverted mass hierarchy (IH) CP trajectory ellipses in the P-P^T plane seems to be very promising as a means of investigating the mass hierarchy. An illustration of the separation between the two hierarchy ellipses in the E-L plane is very helpful to cover all the desired baselines and beam energies and also to analyze the benefits and drawbacks in one step. If we know the mass hierarchy, then, from the large sizes of CP trajectory ellipses that are possible at appropriately long baselines (L) and at specific values of beam energy (E), it becomes possible to investigate at least narrow ranges of the CP/T-violating phase δ^CP. The possibility of more than one set of (θ₁₃,δ^CP) parameters corresponding to any chosen coordinate in the P-P^T plane, known as parameter degeneracy, may hinder the exact determination of the mass hierarchy as well as the δ^CP value. To circumvent this degeneracy in the (θ₁₃,δ^CP) parameter space, in the case of opposite-sign solutions corresponding to the NH and IH cases, sufficiently long baselines are needed, so as to separate the opposite hierarchy ellipses to create an observable separation; in the case of same-sign solutions corresponding to either NH or IH, we need to choose an experimental configuration with L≃2535 km, E≃5 GeV for the n=1 scenario