Absolute Values of Neutrino Masses implied by the Seesaw Mechanism

It is found that the seesaw mechanism not only explain the smallness of neutrino masses but also account for the large mixing angles simultaneously, even if the unification of the neutrino Dirac mass matrix with that of up-type quark sector is realized. We show that provided the Majorana masses have hierarchical structure as is seen in the up-type quark sector and all mass matrices are real, we can reduce the information about the absolute values of neutrino masses through the data set of neutrino experiments. Especially for $\theta_{13}=0$, we found that the neutrino masses are decided as $m_1:m_2:m_3\approx 1:3:17$ or $1:50:250$ ($m_1\simeq m_2:m_3\approx 3:1$ or $12:1$) in the case of normal mass spectrum (inverted mass spectrum), and the greatest Majorana mass turns out to be $m_3^R=1\times 10^{15}$ GeV which just corresponds to the GUT scale. Including the decoupling effects caused by three singlet neutrinos, we also perform a renormalization group analysis to fix the neutrino Yukawa coupling matrix at low energy.