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 Delta m(2) hierarchy and a small admixture of the electron neutrino in the heavy mass eigenstate characterized by the mixing angle theta(13). We show that for Delta m(2) similar or equal to (0.5-3) x 10(-3) eV(2) indicated by the super-Kamiokande data and sin(2) 2 theta(13) less than or similar to 0.2, the oscillations of multi-GeV neutrinos in the subdominant nu(mu) <-> nu(e) 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 Delta m(2) similar or equal to (1-2) x 10(-3) eV(2), sin(2) 2 theta(13) less than or similar to 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 theta(13). The up-down asymmetry of the multi-GeV e-like events can reach 15% for \cos Theta(e)\ > 0.2 and up to 30% for \cos Theta(e)\ > 0.6, where Theta(e) is the zenith angle of the electron. The resonance matter effects are relevant for the interpretation of the super-Kamiokande data. (C) 1999 Elsevier Science B.V.