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

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)x10-3 eV2 indicated by the super-Kamiokande data and sin2 2θ13 < or approx. 0.3, the oscillations of multi-GeV neutrinos in the subdominant νμ ↔ 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)x10-3 eV2, msin2 2θ13 < or approx. 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 parallel cos Θe parallel > 0.2 and up to 30% for parallel cos Θe parallel > 0.6, where Θd is the zenith angle of the electron. The resonance matter effects are relevant for the interpretation of the super-Kamiokande data