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 mu(3)(2) much greater than mu(2)(2) greater than or equal to mu(1)(2), the solution of the atmospheric neutrino problem depends on delta(31) = mu(3)(2) - mu(1)(2) and the 13 and 23 mixing angles phi and psi. Whereas the sub-GeV atmospheric neutrino data imposes only a lower limit on delta(31)>10(-3)eV(2), the zenith-angle-dependent suppression observed in the multi-GeV data limits delta(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 delta(21) = mu(2)(2) - mu(1)(2) and the 12 and 13 mixing angles omega and phi, we have obtained the ranges of values of the five neutrino parameters which solve both the solar and the atmospheric neutrino problems simultaneously.