Theory of Fermion Masses, Mixing, Lagrangian Potentials and Weak Beta Decays, based on Higgs Bosons arising from the Scalar Fields of a Kaluza Klein Theory with Five-Dimensional General Covariance Provided by Dirac’s Quantum Theory of the Electron Jay Yablon To cite this version: Jay Yablon. Theory of Fermion Masses, Mixing, Lagrangian Potentials and Weak Beta Decays, based on Higgs Bosons arising from the Scalar Fields of a Kaluza Klein Theory with Five-Dimensional General Covariance Provided by Dirac’s Quantum Theory of the Electron. 2018. hal-01961238 HAL Id: hal-01961238 https://hal.archives-ouvertes.fr/hal-01961238 Preprint submitted on 19 Dec 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Jay R. Yablon, December 19, 2018 Theory of Fermion Masses, Mixing, Lagrangian Potentials and Weak Beta Decays, based on Higgs Bosons arising from the Scalar Fields of a Kaluza Klein Theory with Five-Dimensional General Covariance Provided by Dirac’s Quantum Theory of the Electron Jay R. Yablon Einstein Centre for Local-Realistic Physics 15 Thackley End Oxford OX2 6LB, United Kingdom [email protected] December 19, 2018 Abstract: Why the twelve elementary fermions have the masses they have (and what the neutrino masses actually are) is one of the deepest unsolved mysteries of modern physics. We crack this puzzle using a theory of fermion masses which succeeds in reparameterizing all twelve fermion masses in terms of other known parameters to which their theoretical interconnections have not heretofore been understood. The first step is to “repair” long-recognized perplexities of Kaluza- Klein theory using Dirac’s quantum theory of the electron to enforce general covariance across all five dimensions. One consequence of this is the emergence of a modified Dirac equation for fermions which naturally contains the Kaluza-Klein scalar. After establishing a connection between this Kaluza-Klein scalar and the standard model Higgs scalar, we use the latter to theoretically connect the known masses of all the quarks and charged leptons to the CKM and PMNS mixing angles and matrix components and several other parameters which have not previously been connected to these masses. Then, after using the Newton gravitational constant and the Fermi vacuum to establish a sum of neutrino masses in the exact range expected from experiments, it also becomes possible to predict the rest masses of the three flavors of neutrino. Also predicted are the existence and rest mass of a second leptonic Higgs boson, and tighter values for several other known parameters including the mass of the established Higgs boson. Uncovered as well, is a deep role for the cosmological neutrino background (CvB) and Higgs fields in triggering and facilitating weak interaction beta decay events. Jay R. Yablon, December 19, 2018 Contents Preface, and Guide for Efficient Reading and Study ...................................................................... 1 1. Introduction – The Incompatibility of Kaluza-Klein and Dirac Theories ................................. 6 PART I: THE MARRIAGE BETWEEN FIVE DIMENSIONAL KALUZA-KLEIN THEORY AND DIRAC’S QUANTUM THEORY OF THE ELECTRON ................................................. 10 2. The Kaluza-Klein Tetrad and Dirac Operators in Four Dimensional Spacetime, and the Covariant Fixing of Gauge Fields to the Photon .......................................................................... 10 3. Derivation of the “Dirac-Kaluza-Klein” (DKK) Five-Dimensional Metric Tensor ................ 16 4. Calculation of the Inverse Dirac-Kaluza-Klein Metric Tensor ................................................ 19 5. The Dirac Equation with Five-Dimensional General Covariance ........................................... 25 6. The Dirac-Kaluza-Klein Metric Tensor Determinant and Inverse Determinant ..................... 28 7. The Dirac-Kaluza-Klein Lorentz Force Motion ...................................................................... 30 8. Luminosity and Internal Second-Rank Dirac Symmetry of the Dirac-Kaluza-Klein Scalar ... 40 9. How the Dirac-Kaluza-Klein Metric Tensor Resolves the Challenges faced by Kaluza-Klein Theory without Diminishing the Kaluza “Miracle,” and Grounds the Now-Timelike Fifth Dimension in Manifestly-Observed Physical Reality ................................................................... 46 10. Pathways for Continued Exploration: The Einstein Equation, the “Matter Dimension,” Quantum Field Path Integration, Epistemology of a Second Time Dimension, and All-Interaction Unification .................................................................................................................................... 51 PART II: THE DIRAC-KALUZA-KLEIN SCALAR, THE HIGGS FIELD, AND A THEORY OF FERMION MASSES, MIXING AND WEAK BETA DECAYS WHICH RUBUSTLY FITS THE EXPERIMENTAL DATA ................................................................................................... 59 11. Spontaneous Symmetry Breaking of the Massless Luminous Dirac-Kaluza-Klein Scalar, and Integration to Deduce its Spacetime Behavior .............................................................................. 59 12. The Fifth-Dimensional Component of the Dirac-Kaluza-Klein Energy Momentum Vector 69 13. Connection between the Dirac-Kaluza-Klein Scalar and the Higgs Field, and the Extraction of Energy from the Higgs Field by the Top Quark ....................................................................... 74 PART IIA: QUARKS ................................................................................................................... 81 14. Theory of Fermion Masses and Mixing: Up, Charm and Top Quarks .................................. 81 15. Theory of Fermion Masses and Mixing: Down, Strange and Bottom Quarks ...................... 90 16. Theoretical Relation amongst the Higgs Mass and the Isospin-Up and Isospin-Down Quark vevs; and the Two-Minimum, Two Maximum Lagrangian Potential for Quarks ...................... 101 17. The Role of the Higgs Boson and its Mass in Weak Beta-Decays Between Quarks .......... 117 18. The CKM Quark Mixing Matrix Mass Parameterization, and the Fine-Tuning of Quark Masses, Mixing Angles and CKM Matrix Components ............................................................. 122 PART IIB: LEPTONS ................................................................................................................ 136 Jay R. Yablon, December 19, 2018 19. Theory of Fermion Masses and Mixing: Electron, Mu and Tau Charged Leptons ............. 136 20. Theory of Fermion Masses and Mixing: Prediction of the Neutrino Mass Sum and of the Individual Neutrino Masses ........................................................................................................ 145 21. Prediction of a Second Leptonic Higgs Boson, and its Mass .............................................. 152 22. The Two-Minimum, Two Maximum Lagrangian Potential for Leptons ............................. 155 PART IIC: COMPLETE THEORY OF WEAK BETA DECAY .............................................. 162 23. How Weak Beta Decays are Triggered by Cosmological Neutrinos and Antineutrinos Interacting with Electrons, Neutrons and Protons via the Z Boson-Mediated Weak Neutral Current, with “Chiral Polarization” of Electrons ........................................................................ 162 Conclusion .................................................................................................................................. 190 References ................................................................................................................................... 191 Jay R. Yablon, December 19, 2018 Preface, and Guide for Efficient Reading and Study Preface This manuscript is two papers in one. One is about Kaluza-Klein Theory. The other is about particles physics and the rest masses and weak beta decays of the elementary fermions. This began as an effort to “repair” five-dimensional Kaluza-Klein theory in advance of its 2019 centenary, by using Dirac’s Quantum Theory of the Electron as the basis for requiring Kaluza- Klein theory to be generally-covariant across all five of its dimensions. Unexpectedly, this turned into a theory through which it became possible to explain all twelve of the observed elementary fermion masses in relation to other heretofore independent parameters including the CKM and PMNS mixing angles. Of course, Kaluza-Klein theory started in 1919 as a classical theory to unify Maxwell’s electrodynamics with general relativistic gravitation, before we even had modern gauge theory or Dirac theory or much of modern quantum theory. Because one would not normally expect to be talking about Kaluza-Klein theory and the elementary fermion masses of modern particle physics in the same breath – much less claim that a detailed study of Kaluza-Klein theory can lead to a deep understanding of these fermion masses – it is important to overview the trail that led from one to the other, and why it is that this is all best-presented in one complete