Neutrino mass hierarchy and \delta^{CP} investigation within the biprobability (P-P^T ) plane

This article illustrates the possibility of investigating mass hierarchy and CP-violating phase \delta^{CP}, in the context of CP trajectory diagrams in the bi-probability plane. Separation between normal mass hierarchy (NH) and inverted mass hierarchy (IH) CP trajectory ellipses in the P-P^T plane seems to be very promising in order to investigate mass hierarchy. Illustration of separation between two hierarchy ellipses in the E-L plane is very helping to cover all the desired base lines and beam energies and also to analyze benefits and drawbacks at single place. If we know the mass hierarchy, then from the large sizes of CP trajectory ellipse which is possible at appropriately long base line (L) and at specific value of beam energy (E), it becomes possible to investigate at-least narrow ranges of CP/T-violating phase \delta^{CP}. The Possibility of more than one set of (\theta_{13}; \delta^{CP}) parameters to correspond to any chosen coordinate in P-P^T plane, known as parameter degeneracy, may hinder exact determination of mass hierarchy as well as \delta^{CP} value. To circumvent this degeneracy in the (\theta_{13}; \delta^{CP}) parameter space, in case of opposite sign solutions corresponding to NH and IH case points toward the need of sufficiently long base lines, so as to separate opposite hierarchy ellipses to observable separation, and in case of same sign solutions corresponding to either NH or IH, we need to choose an experimental configuration with L = 2,535 Km, E = 5 GeV for n=1 scenario.