Neutrino oscillations with two Δm2 scales -: art. no. 050

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, Deltam(2), of neutrino mass squared differences, in particular, Deltam(atm)(2) similar to 3 x 10(3) eV(2). Here we investigate the corrections to this approximation arising from the quantity Deltam(sol)(2) relevant for solar neutrino oscillations, assuming the large mixing angle solution. We show that for values of sin(2)(2theta(13)) similar to 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 Deltam(sol)(2) similar to 10(4) eV(2), the contributions to nu(mu) --> nu(e) oscillations from both CP-conserving and CP-violating terms involving sin(2)(Deltam(sol)(2)L/(4E)) can be comparable to the terms involving sin(2)(Deltam(atm)(2)L/(4E)) retained in the one-Deltam(2) approximation. Accordingly, we emphasize the importance of performing a full three-flavor, two-Deltam(2) analysis of the data on nu(mu) --> nu(e) oscillations in a conventional-beam experiment and nu(e) --> nu(mu), (nu) over bar (e) --> (nu) over bar (mu) 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 nu(mu) --> nu(e) oscillations. Finally, we consider the analysis of atmospheric neutrino data and present calculations of matter erects in a three-flavor, two-Deltam(2) framework relevant to this data and to neutrino factory measurements.