Comparing and contrasting the ν_μ→ν_τ and ν_μ→ν_s solutions to the atmospheric neutrino problem with SuperKamiokande data

The ν_μ→ν_τ and ν_μ→ν_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 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 normalization and detection cross sections and efficiencies. A χ² analysis using these quantities is performed yielding 3σ ranges which are approximately given by (0.725–1.0, 4×10^-4–2×10^-2 eV²) and (0.74–1.0, 1×10^-3–2×10^-2 eV²) for (sin²2θ,Δm²) for the ν_μ→ν_τ and ν_μ→ν_s solutions, respectively. Values of Δm² smaller than about 2×10^-3 eV² are disfavored for the ν_μ→ν_s solution, suggesting that future long baseline experiments should see a positive signal if this scenario is the correct one.