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

Abstract

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 vμ→ve 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, (Δ θ/θ̄), 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 CPIT trajectory diagrams are extensively used to illuminate the nature of the degeneracies. © 2002 The American Physical Society.