Neutrino oscillation probabilities: sensitivity to parameters

Abstract

We study in detail the sensitivity of neutrino oscillation probabilities to the fundamental neutrino parameters and their possible determination through experiments. The first part of the paper is devoted to the broad theme of isolating regions in the neutrino (and antineutrino) energy and propagation length that are sensitive to the oscillation parameters. Such a study is relevant to neutrinos both from the Earth's atmosphere or from a neutrino factory. For completeness we discuss the sensitivity, however small, to the parameters involved in a three-generation framework, and to the Earth matter density profile. We then study processes relevant to atmospheric neutrinos which are sensitive to and allow precision measurements of the mixing angle θ ₂₃ and mass-squared difference δ₃₂ apart from the mixing angle θ ₁₃. Crucial to this analysis is charge identification; detectors having this capability can isolate these matter effects. In particular, we address the issue of using matter effects to determine whether the mixing angle θ₂₃ is maximal, and, if not, to explore how well its octant can be determined. When realistic detector resolutions are included, we find that deviations of about 15% (20%) from a maximal value of sin²θ₂₃=½ can be measured at 95% (99%) C.L. provided θ₁₃ is nonzero, sin²θ₁₃≥0.015, and the neutrino mass ordering is normal, with fairly large exposures of 1000 kton-years.