Comparing and contrasting the ν μ → ν τ and ν μ → ν s solutions to the atmospheric neutrino problem with SuperKamiokande data

The νμ → ντ and νμ → νs 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 μ-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 χ analysis using these quantities is performed yielding 3σ ranges which are approximately given by (0.725−1.0, 4×10−4−2×10−2 eV ) and (0.74−1.0, 1×10−3−2×10−2 eV ) for (sin 2θ,∆m) for the νμ → ντ and νμ → νs solutions, respectively. Values of ∆m smaller than about 2 × 10 eV are disfavoured for the νμ → νs solution, suggesting that future long baseline experiments should see a positive signal if this scenario is the correct one.