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An approximation that is often used in fits to reactor and atmosphericneutrino data and in some studies of future neutrino oscillation experiments isto assume one dominant scale, $\Delta m^2$, of neutrino mass squareddifferences, in particular, $\Delta m^2_{atm} \sim 3 \times 10^{-3}$ eV$^2$.Here we investigate the corrections to this approximation arising from thequantity $\Delta m^2_{sol}$ relevant for solar neutrino oscillations, assumingthe large mixing angle solution. We show that for values of$\sin^2(2\theta_{13}) \sim 10^{-2}$ (in the range of interest for long-baselineneutrino oscillation experiments with either intense conventional neutrinobeams such as JHF-SuperK or a possible future neutrino factory) and for $\Deltam^2_{sol} \sim 10^{-4}$ eV$^2$, the contributions to $\nu_\mu \to\nu_e$oscillations from both CP-conserving and CP-violating terms involving$\sin^2(\Delta m^2_{sol}L/(4E))$ can be comparable to the terms involving$\sin^2(\Delta m^2_{atm}L/(4E))$ retained in the one-$\Delta m^2$approximation. Accordingly, we emphasize the importance of performing a fullthree-flavor, two-$\Delta m^2$ analysis of the data on $\nu_\mu \to \nu_e$oscillations in a conventional-beam experiment and $\nu_e \to \nu_\mu$,$\bar\nu_e \to \bar\nu_\mu$ oscillations at a neutrino factory. We also discussa generalized analysis method for the KamLAND reactor experiment, and note howthe information from this experiment can be used to facilitate the analysis ofthe subsequent data on $\nu_\mu \to \nu_e$ oscillations. Finally, we considerthe analysis of atmospheric neutrino data and present calculations of mattereffects in a three-flavor, two-$\Delta m^2$ framework relevant to this data andto neutrino factory measurements.Comment: 24 pages, revtex, 5 postscript figures, some refs. adde

Neutrino Oscillations with Two Δm2 Scales

Neutrino Oscillations with Two Δm² Scales