Atmospheric neutrinos with three flavor mixing

Abstract

We analyze the atmospheric neutrino data in the context of three flavor neutrino oscillations taking account of the matter effects in the earth. With the hierarchy among the vacuum mass eigenvalues $μ_3^2 \gg μ_2^2 \geq μ_1^2$, the solution of the atmospheric neutrino problem depends on $δ_{31}=μ_3^2 - μ_1^2$ and the $13$ and $23$ mixing angles $ϕ$ and $ψ$. Whereas the sub-GeV atmospheric neutrino data imposes only a lower limit on $δ_{31} > 10^{-3} eV^2$, the zenith angle dependent suppression observed in the multi-GeV data limits $δ_{31}$ from above also. The allowed regions of the parameter space are strongly constrained by the multi-GeV data. Combined with our earlier solution to the solar neutrino problem which depends on $δ_{21}= μ_2^2-μ_1^2$ and the $12$ and $13$ mixing angles $ω$ and $ϕ$, we have obtained the ranges of values of the five neutrino parameters which solve both the solar and the atmospheric neutrino problems simultaneously.