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 [Formula presented], the solution of the atmospheric neutrino problem depends on [Formula presented] and the [Formula presented] and [Formula presented] mixing angles [Formula presented] and [Formula presented]. Whereas the sub-GeV atmospheric neutrino data imposes only a lower limit on [Formula presented], the zenith-angle-dependent suppression observed in the multi-GeV data limits [Formula presented] 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 [Formula presented] and the [Formula presented] and [Formula presented] mixing angles [Formula presented] and [Formula presented], we have obtained the ranges of values of the five neutrino parameters which solve both the solar and the atmospheric neutrino problems simultaneously. © 1997 The American Physical Society.