Analysis of atmospheric neutrino oscillations in three-flavor neutrinos

We analyze the atmospheric neutrino experiments of Super-Kamiokande (830-920 live days) using the three-flavor neutrino framework with the mass hierarchy m_1 nearly equal m_2 << m_3. We study the sub-GeV, multi- GeV neutrinos and upward through-going and stopping muons zenith angle distributions taking account of the Earth matter effects thoroughly. We obtain the allowed regions of mass and mixing parameters Delm^2_{23}, theta_{13} and theta_{23}. Delm^2_{23} is restricted to 0.002-0.01eV^2 and theta_{13}<13degrees, 35degrees<theta_{23}<55degrees in 90% C.L. For theta_{12}, there is no difference between the large angle solar neutrino solution and small one. From chi^2 fit, the minimum chi^2=55(54DOF) is obtained at Delm^2_{23}=4x10^(-3)eV^2, theta_{13}=10degrees and theta_{23} =45degrees.