Quadratic Hierarchy Flavor Rule as the Origin of Dirac CP-Violating Phases

Abstract

The premise of an organizing quadratic hierarchy rule in lepton-quark flavor physics was used earlier for explanation of the hierarchy patterns of four generic pairs of flavor quantities 1) charged-lepton and 2) neutrino deviations from mass-degeneracy, 3) deviations of lepton mixing from maximal magnitude and 4) deviations of quark mixing from minimal one. Here it is shown that the quadratic hierarchy equation that is uniquely related to three flavor particle generations may have yet another important function. It determines two complementary values of the Dirac CP-violating phases in the quark and neutrino mixing matrices without involvement of any empirical parameters. If confirmed by accurate experimental data, it means a discovery of an explicit CP-violation source in elementary particle mixing matrices and a single source of CP-violation at least in the quark mass matrix phenomenology.