Atmospheric neutrinos at super-Kamiokande and parametric resonance in neutrino oscillations

Abstract

We consider the oscillations of atmospheric neutrinos in the earth in the three-neutrino scheme with a Δm² hierarchy and a small admixture of the electron neutrino in the heavy mass eigenstate characterized by the mixing angle θ₁₃. We show that for Δm² ~- (0.5−3) × 10⁻³ eV² indicated by the super-Kamiokande data and sin² 2θ₁₃ ⪅ 0.3, the oscillations of multi-GeV neutrinos in the subdominant ν_μ ↔ θ₃ mode are enhanced by the MSW and parametric resonances .The parametric resonance, which occurs when the neutrinos cross the core of the earth, dominates for Δm² ⋍ (1–2) × 10⁻³ eV², msin² 2θ₁₃ ≲ 0.06. The resonance matter effects lead to an observable excess of the e-like events with a specific zenith angle dependence even for small θ₁₃. The updown asymmetry of the multi-GeV e-like events can reach 15% for ∥ cosΘ_e∥ > 0.2 and up to 30% for ∥ cosΘ_e∥ > 0.6, where Θ_d is the zenith angle of the electron. The resonance matter effects are relevant for the interpretation of the super-Kamiokande data.