The Conformal Origin of the Lepton Flavor Mixing Matrix

Abstract

Using the formalism of the flavor spin theory, we re-derive the TM1 lepton flavor mixing factor decomposition in a novel way, using a previously unreported near identity involving the elements of the first row of U_PMNS. The resulting mixing matrix is a direct consequence of the conformal symmetry of the massless SM before the EW phase transition. In addition to the previously reported results, we derive a relation between the CP violating phase and the three mixing angles. Application of the relation to the experimental data data suggests the TM1 decomposition should use (19/12)Pi as the value for the CP violating phase. With this assumption all four parameters of TM1 may be expressed in radicals, which might help in the separation of the classical values of the mixing parameters from their quantum corrections in the framework of the flavor spin theories. This in turn could help in clarification of the mass generation mechanism.