Neutrino Oscillations with Two $\Delta m^2$ Scales

Abstract

An approximation that is often used in fits to reactor and atmospheric neutrino data and in some studies of future neutrino oscillation experiments is to assume one dominant scale, $\Delta m^2$, of neutrino mass squared differences, in particular, $\Delta m_{atm}^2\sim 3\times 10^{-3}$ eV${}^2$. Here we investigate the corrections to this approximation arising from the quantity $\Delta m_{sol}^2$ relevant for solar neutrino oscillations, assuming the 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-baseline neutrino oscillation experiments with either intense conventional neutrino beams such as JHF-SuperK or a possible future neutrino factory) and for $\Delta m_{sol}^2\sim 10^{-4}$ eV${}^2$, the contributions to ${\nu }_{\mu }\to {\nu }_e$ oscillations from both CP-conserving and CP-violating terms involving ${\sin }^2(\Delta m_{sol}^{2}L/(4E))$ can be comparable to the terms involving ${\sin }^2(\Delta m_{atm}^{2}L/(4E))$ retained in the one-$\Delta m^2$ approximation. Accordingly, we emphasize the importance of performing a full three-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 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 ${\nu }_{\mu }\to {\nu }_e$ oscillations. Finally, we consider the analysis of atmospheric neutrino data and present calculations of matter effects in a three-flavor, two-$\Delta m^2$ framework relevant to this data and to neutrino factory measurements.

24 pages, revtex, 5 postscript figures, some refs. added

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