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, Δm_atm ² ∼ 3 × 10^-3 eV². Here we investigate the corrections to this approximation arising from the quantity Δm_sol ² relevant for solar neutrino oscillations, assuming the large mixing angle solution. We show that for values of sin²(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 Δm_sol ² ∼ 10^-4 eV², the contributions to v_μ → v_e oscillations from both CP-conserving and CP-violating terms involving sin²(Δm_sol ²L/(4E)) can be comparable to the terms involving sin²(Δm_atm ²L/(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 v_μ → v_e oscillations in a conventional-beam experiment and v_e → v_μ, v_e → v_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 v_μ → v_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.