CP and T Trajectory Diagrams for a Unified Graphical Representation of Neutrino Oscillations

Abstract

Recently the CP trajectory diagram was introduced to demonstrate the difference between the intrinsic CP violating effects to those induced by matter for neutrino oscillation. In this paper we introduce the T trajectory diagram. In these diagrams the probability for a given oscillation process is plotted versus the probability for the CP- or the T-conjugate processes, which forms an ellipse as the CP or T violating phase is varied. Since the CP and the T conjugate processes are related by CPT symmetry, even in the presence of matter, these two trajectory diagrams are closely related with each other and form a unified description of neutrino oscillations in matter.