Three flavor implications of CHOOZ result

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Abstract
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 a hierarchy among the vacuum mass eigenvalues (\delta_{21} \ll \delta_{31}), then the CHOOZ result limits the (13) mixing angle \phi to quite small values. This in turn limits the contribution of the \nu_e <--> \nu_\mu oscillation channel to the atmospheric neutrino anomaly to less than 10 percent. It also implies that the solution to the solar neutrino problem is effectively \nu_e <--> \nu_\mu oscillation and that of the atmospheric neutrino problem is effectively \nu_\mu <--> \nu_\tau.

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