Comparing and contrasting the $\hat{I}{½}_{\hat{I}}¼\to \hat{I}{½}_{\ddot{I}}„$ and $\hat{I}{½}_{\hat{I}}¼\to \hat{I}{½}_s$ solutions to the atmospheric neutrino problem with SuperKamiokande data

Abstract

The $\hat{I}{½}_{\hat{I}}¼\to \hat{I}{½}_{\ddot{I}}„$ and $\hat{I}{½}_{\hat{I}}¼\to \hat{I}{½}_s$ solutions to the atmospheric neutrino problem are compared with SuperKamiokande data. The differences between these solutions due to matter effects in the Earth are calculated for the ratio of $\hat{I}¼$-like to $e$-like events and for up-down flux asymmetries. These quantities are chosen because they are relatively insensitive to theoretical uncertainties in the overall neutrino flux normalisation and detection cross-sections and efficiencies. A $\ddot{I}{‡}^2$ analysis using these quantities is performed yielding $3\ddot{I}ƒ$ ranges which are approximately given by $(0.725-1.0,4\times 10^{-4}-2\times 10^{-2}e{V}^2)$ and $(0.74-1.0,1\times 10^{-3}-2\times 10^{-2}e{V}^2)$ for $({\sin }^{2}2\hat{I}¸,\hat{I}”m^2)$ for the $\hat{I}{½}_{\hat{I}}¼\to \hat{I}{½}_{\ddot{I}}„$ and $\hat{I}{½}_{\hat{I}}¼\to \hat{I}{½}_s$ solutions, respectively. Values of $\hat{I}”m^2$ smaller than about $2\times 10^{-3}$ eV${}^2$ are disfavoured for the $\hat{I}{½}_{\hat{I}}¼\to \hat{I}{½}_s$ solution, suggesting that future long baseline experiments should see a positive signal if this scenario is the correct one.

revtex, 22 pages, 12 figures