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

2007/10/22 by É. M. Lipmanov, E. M. Lipmanov, Lipmanov, E. M. · 1 citation
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Neutrino Physics Research #Particle physics theoretical and experimental studies #hep-ph

paper · pdf · doi:10.48550/arxiv.0710.4125

8 pages

openalex publication_date 2007/10/22 · arxiv created 2007/10/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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