Neutrino Oscillations with Two Δm² Scales

An approximation that is often used in fits to reactor and atmospheric neutrino data and in some theoretical studies is to assume one dominant scale, Δm², of neutrino mass squared differences, in particular, Δm²_atm ∼ 3 × 10⁻³ eV². Here we investigate the corrections to this approximation arising from the quantity Δm²_sol relevant for solar neutrino oscillations, assuming the large mixing angle solution. We show that for values of sin ²(2θ₁₃) ∼ 10⁻² (in the range of interest for long-baseline neutrino oscillation experiments with either intense conventional neutrino beams such as JHF-SuperK or a possible future neutrino factory) and for Δm²_sol ∼ 10⁻⁴ eV², the contributions to ν_μν_e oscillations from both CP-conserving and CP-violating terms involving sin ²(Δm²_solL/(4E)) can be comparable to the terms involving sin ²(Δm²_atmL/(4E)) retained in the one-Δm² approximation. Accordingly, we emphasize the importance of performing a full three-flavor, two-Δm² analysis of the data on ν_μν_e oscillations in a conventional-beam experiment and ν_eν_μ, _e_μ oscillations at a neutrino factory. We also discuss a generalized analysis method for the KamLAND reactor experiment, and note how the information from this experiment can be used to facilitate the analysis of the subsequent data on ν_μν_e oscillations. Finally, we consider the analysis of atmospheric neutrino data and present calculations of matter effects in a three-flavor, two-Δm² framework relevant to this data and to neutrino factory measurements.