Parameter Degeneracies in Neutrino Oscillation Measurement of Leptonic CP and T Violation

Abstract

The measurement of the mixing angle \theta_{13}, sign of \Delta m^2_{13} and the CP or T violating phase \delta is fraught with ambiguities in neutrino oscillation. In this paper we give an analytic treatment of the paramater degeneracies associated with measuring the \nu_\mu -> \nu_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 two-fold and four-fold degeneracies. We calculate the fractional differences, \Delta \theta / \bar{\theta}, 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 \Delta m^2_{13} 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 four fold parameter degeneracy apart from exceptional points. Explicit solutions are also given and the fractional differences are computed. The bi-probability CP/T trajectory diagrams are extensively used to illuminate the nature of the degeneracies.