Three flavor implications of the result of the CHOOZ Collaboration

We analyze the recent result of the CHOOZ Collaboration in the context of mixing and oscillations between all the three neutrino flavors. If one assumes the hierarchy among the vacuum mass eigenvalues ${\delta }_{21}\ll {\delta }_{31}$ where ${\delta }_{21}={\mu }_2^2-{\mu }_1^2$ and ${\delta }_{31}={\mu }_3^2-{\mu }_1^2,$ then the CHOOZ result puts a strong constraint on the allowed values of the (13) mixing angle φ. It is also shown that, in light of the CHOOZ result, the maximum contribution of the ${\nu }_{\mu }\leftrightarrow {\nu }_e$ oscillation channel to the atmospheric neutrino anomaly is less than 7 percent, thus demonstrating that the atmospheric neutrino anomaly is mainly due to ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ oscillations. Most importantly the CHOOZ result now excludes a large part of the three flavor parameter space which was previously allowed as solutions to the solar and atmospheric neutrino problems.