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) much less than delta(31) Where delta(21) = mu(22) - 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 phi. It is also shown that, in light of the CHOOZ result, the maximum contribution of the nu(mu) <-> 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) <-> 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. [S0556-2821(98)50415-8]