Neutrino masses and mixings in a seesaw framework

Assuming the seesaw mechanism for hierarchical neutrino masses, we calculate the heavy neutrino masses under the hypotheses that the mixing in the Dirac leptonic sector is similar to the quark mixing ($V_D \sim V_{CKM}$) and that $M_{\nu} \sim M_u$ or $M_e$, where $M_{\nu}$ is the Dirac mass matrix of neutrinos. As a result we find that for $M_{\nu} \sim M_u$ the vacuum oscillation solution of the solar neutrino problem leads to a scale for the heavy neutrino mass well above the unification scale, while for the MSW solutions there is agreement with this scale. For $M_{\nu} \sim M_e$ the vacuum solution is consistent with the unification scale, and the MSW solutions with an intermediate scale. The mass of the lightest heavy neutrino can be as small as $10^5$ GeV.