CP trajectory diagram—a tool for a pictorial representation of CP and matter effects in neutrino oscillations

We introduce a “CP trajectory diagram in bi-probability space” as a powerful tool for a pictorial representation of the genuine CP and the matter effects in neutrino oscillations. The existence of correlated ambiguity in the determination of CP-violating phase δ and the sign of Δm132 is uncovered. The principles of tuning the beam energy for a given baseline distance are proposed to resolve the ambiguity and to maximize the CP-odd effect. We finally point out, quite contrary to what is usually believed, that the ambiguity may be resolved with ∼50% chance in the super-JHF experiment despite its relatively short baseline of 300 km.