Relation between CKM and MNS Matrices Induced by Bi-Maximal Rotations in the Seesaw Mechanism

Abstract

It is found that the seesaw mechanism not only explains the smallness of neutrino masses but also accounts 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. In this mechanism, we show that the mixing matrix of the Dirac-type mass matrix gets extra rotations from the diagonalization of Majorana mass matrix. Assuming that the mixing angles to diagonalize the Majorana mass matrix are extremely small, we find that the large mixing angles of leptonic sector found in atmospheric and long baseline reactor neutrino oscillation experiments can be explained by these extra rotations. We also find that provided the mixing angle around y-axis to diagonalize the Majorana mass matrix vanishes, we can derive the information about the absolute values of neutrino masses and Majorana mass responsible for the neutrinoless double beta decay experiment through the data set of neutrino experiments. In the simplified case that there is no CP phase, we find that the neutrino masses are decided as $m_1:m_2:m_3\approx 1:2:8$ and that there are no solution which satisfy $m_3<m_1<m_2$ (inverted mass spectrum). Then, including all CP phases, we reanalyze the absolute values of neutrino masses and Majorana mass responsible for the neutrinoless double beta decay experiment.