Parameter degeneracies in neutrino oscillation measurement of leptonic CP and T violation

The measurement of the mixing angle θ₁₃, sign of Δm₁₃², and the CP or T violating phase δ is fraught with ambiguities in neutrino oscillation. In this paper we give an analytic treatment of the paramater degeneracies associated with measuring the ν_μ→ν_e probability and its CP and/or T conjugates. For CP violation, we give explicit solutions to allow us to obtain the regions where there exist twofold and fourfold degeneracies. We calculate the fractional differences, (Δθ/θ̅ ), between the allowed solutions which may be used to compare with the expected sensitivities of the experiments. For T violation we show that there is always a complete degeneracy between solutions with positive and negative Δm₁₃² which arises due to a symmetry and cannot be removed by observing one neutrino oscillation probability and its T conjugate. Thus there is always a fourfold parameter degeneracy apart from exceptional points. Explicit solutions are also given and the fractional differences are computed. The biprobability CP/T trajectory diagrams are extensively used to illuminate the nature of the degeneracies.