Neutrino oscillation probabilities: Sensitivity to parameters

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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 anti-neutrino) 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 theta₂3 and mass-squared difference delta₃2 apart from the mixing angle theta₁3. 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 theta₂3 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 sin² theta₂3=1/2 can be measured at 95% (99%) CL provided theta₁3 is non-zero, sin² theta₁3 >= 0.015, and the neutrino mass ordering is normal, with fairly large exposures of 1000 kton-years.