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 Δm 2 hierarchy and a small admixture of the electron neutrino in the heavy mass eigenstate characterized by the mixing angle θ 13. We show that for Δm 2 ∼- (0.5−3) × 10 −3 eV 2 indicated by the super-Kamiokande data and sin 2 2θ 13 ⪅ 0.3, the oscillations of multi-GeV neutrinos in the subdominant ν μ ↔ θ 3 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 Δm 2 ⋍ (1–2) × 10 −3 eV 2 , msin 2 2θ 13 ≲ 0.06 . The resonance matter effects lead to an observable excess of the e-like events with a specifcic zenith angle dependence even for small θ 13. The updown asymmetry of the multi-GeV e-like events can reach 15% for ∥ cos Θ e ∥ > 0.2 and up to 30% for ∥ cos Θ 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.