Triangular mass matrices for quarks and leptons

Abstract

We assume that all quark and lepton $3 \times 3$ mass matrices which appear in the standard model lagrangian (after spontaneous symmetry breaking) with neutrinos treated as Dirac patricles have the triangular form. Such matrices have not only less non-zero elements (three of them are equal to zero) but also lead to very asymmetrical decomposition into one diagonal and two unitary matrices for quarks and leptons. We also assume that unitary matrices which transform flavor into definite mass states for right handed components (weakly non-interacting) in the same weak isodoublet are equal. Using all available experimental data on quark and lepton masses and mixing angles, treating in the universal way quarks and leptons, we determine the triangular mass matrices for up and down type quarks, neutrinos and charged leptons and as a consequence mixing matrices for left-handed and right handed components. As the result of the fit we get predictions for the neutrino masses including smallest neutrino mass. The calculations without CP violation and with inclusion of this effect in quark sector are also presented.