Determining quark and lepton mass matrices by a geometrical interpretation

By designating one eigenvector of the mass matrix, one can reduce the free parameters in the mass matrix effectively. Applying this method to the quark mass matrix and to the lepton mass matrix, we find that this method is consistent with available experimental data. This approach may provide some hints for constructing theoretical models. Especially, in the lepton sector, the Koide’s mass relation is connected to the element of the tribimaximal matrix through Foot’s geometrical interpretation. In the quark sector, we suggest another mass formula and the same procedure also applies.