Neutrino mixing in the seesaw model

In the seesaw model with hierarchical Dirac masses, the neutrino mixing angle exhibits the behavior of a narrow resonance. In general, the angle is strongly suppressed, but it can be maxima tor special parameter values. We delineate the small regions in which this happens for the two-flavor problem. On the other hand, the physical neutrino masses are hierarchical, in general, except in a large part of the region in which the mixing angle is sizable, where they are nearly degenerate. Our general analysis is also applicable to the RGE of the neutrino mass matrix, where we find analytic solutions for the running of the physical parameters, in addition to a complex RGE invariant relating them. It is also shown that, if one mixing angle is small, the three-neutrino problem reduces to two two-flavor problems.