Three flavor neutrino oscillation analysis of the kamiokande multi-gev atmospheric neutrino data

Abstract

Using the published Kamiokande data of the multi-GeV atmospheric neutrinos, we have searched the optimum set of the neutrino oscillation parameters among three flavors. It is found that $\chi^2$ is minimized for ($\Delta m_{21}^2$, $\Delta m_{31}^2$) = (3.8$\times 10^{-2}~$eV$^2$, 1.4$\times 10^{-2}~$eV$^2$), ($\theta_{12}$, $\theta_{13}$, $\theta_{23}$) = ($19^\circ$,$43^\circ$,$41^\circ$) with $\chi_{\rm min}$ = 3.2 (42\%CL). The sets of parameters ($\Delta m_{21}^2$, $\Delta m_{31}^2$) = (${\cal O}$($10^{-11}$eV$^2$) or ${\cal O}$($10^{-5}$eV$^2$), ${\cal O}$($10^{-2}$eV$^2$)) which are suggested by the two flavor analysis fall within 0.7$\sigma$.