Left-Right symmetric fermions and sterile neutrinos from complex split biquaternions and bioctonions

Abstract

In this article we investigate the application of complex split biquaternions and bioctonions to the standard model. We show that the Clifford algebras Cl(3) and Cl(7) can be used for making left-right symmetric fermions. Hence we incorporate right-handed neutrinos in the division algebras based approach to the standard model. The right-handed neutrinos, also known as sterile neutrinos, are a potential dark-matter candidate. We discuss the left-right symmetric fermions and their phenomenology using the division algebra approach. We describe the gauge groups associated with the left-right symmetric model and prospects for unification through division algebras. We investigate the possibility of obtaining three generations of fermions and charge/mass ratios through the exceptional Jordan algebra $J_3(O)$ and the exceptional groups $F_4$ and $E_6$.

arXiv comment20 pages, 2 figures, accepted for publication in Advances in Applied Clifford algebras

References in corpus (23)

• Evidence for oscillation of atmospheric neutrinos
• Direct Evidence for Neutrino Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory
• General Relativity in terms of Dirac Eigenvalues
• Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra
• Exceptional quantum geometry and particle physics
• Implications of Higgs Discovery for the Strong CP Problem and Unification
• Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra
• $SU(3{)}_C\times SU(2{)}_L\times U(1{)}_Y\left(\times U(1{)}_X\right)$ as a symmetry of division algebraic ladder operators
• Dimensional Reduction
• Three fermion generations with two unbroken gauge symmetries from the complex sedenions
• The Standard Model, The Exceptional Jordan Algebra, and Triality
• The Standard Model Algebra - Leptons, Quarks, and Gauge from the Complex Clifford Algebra Cl6
• Majorana Neutrinos, Exceptional Jordan Algebra, and Mass Ratios for Charged Fermions
• Trace dynamics and division algebras: towards quantum gravity and unification
• Higgs Parity Grand Unification
• Octions: An $E_8$ description of the Standard Model
• A Geometric Approach to the Standard Model
• Why does the Kerr-Newman black hole have the same gyromagnetic ratio as the electron?
• Subgroups of Clifford algebras
• Proposal for a new quantum theory of gravity III: Equations for quantum gravity, and the origin of spontaneous localisation
• Quantum gravity effects in the infra-red: a theoretical derivation of the low energy fine structure constant and mass ratios of elementary particles
• From quantum foundations, to spontaneous quantum gravity: an overview of the new theory
• Neutrino: chronicles of an aloof protagonist

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• An Algebraic Roadmap of Particle Theories, Part II: Theoretical checkpoints
• An Algebraic Roadmap of Particle Theories, Part I: General construction
• A Proposed $E_8\times E_8$ Kinematic Scaffolding for the Standard Model with Pre-Gravitation
• Division Algebras, Triality, and Exceptional Magic