General 4–zero texture mass matrix parametrizations

It is performed the diagonalization of a non–Hermitian four–zero texture Yukawa matrix with a general formalism. This procedure leads to 3 possibilities to parametrize the relation between the fermion masses and the elements of the corresponding Yukawa matrix. Then, the matrices that diagonalize each Yukawa mass matrix are combined in order to obtain 9 different theoretical CKM or PMNS mixing matrices [1]. Through a χ2 analysis, we have constrained the values of the remaining free parameters such as the theoretical mixing matrix matches the latest experimental measurements of the mixing matrices. This analysis was done without assuming any approximations. In the case of the quark sector, it is found that only four different theoretical mixing matrices are compatible with the actual high precision experimental measurement of the CKM matrix elements. For the lepton sector, where the masses of neutrinos are not known, we found that independently of the parametrization that have been chosen, the updated experimental measurements of the mixing angles in the PMNS matrix, imply a mass for the heaviest left–handed neutrino to be ~ 0.05eV.