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 $\Delta m^2$ 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 $\Delta m^2\simeq (0.5-3)\times 10^{-3}$ eV${}^2$ indicated by the Super-Kamiokande data and ${\sin }^{2}2{\theta }_{13}\text{aprle}0.2$, the oscillations of multi-GeV neutrinos in the subdominant ${\nu }_{\mu }\leftrightarrow {\nu }_e$ 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 $\Delta m^2\simeq (1-2)\times 10^{-3}$ eV${}^2$, ${\sin }^{2}2{\theta }_{13}\text{aprle}0.06$. 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.

Comments: LaTex, 48 pages, 16 figures. Substantial changes; new figure added