Constraints on three-neutrino mixing from atmospheric and reactor data

Observations of atmospheric neutrinos are usually analyzed using the simplifying approximation that either ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ or ${\nu }_e\leftrightarrow {\nu }_{\mu }$ two-flavor mixing is relevant. Here we instead consider the data using the simplifying approximation that only one neutrino mass scale is relevant. This approximation is the minimal three-flavor notat on that includes the two relevant two-flavor approximations. The constraints in the parameter space orthogonal to the usual, two-flavor analyses are studied.