The flavor symmetry in the standard model and the triality symmetry

Abstract

A Dirac fermion is expressed by a 4 component spinor which is a combination of two quaternions and which can be treated as an octonion. The octonion possesses the triality symmetry, which defines symmetry of fermion spinors and bosonic vector fields. The triality symmetry relates three sets of spinors and two sets of vectors, which are transformed among themselves via transformations $G_{23},G_{12},G_{13}$, $G_{123}$ and $G_{132}$. If the electromagnetic (EM) interaction is sensitive to the triality symmetry, i.e. EM probe selects one triality sector, EM signals from the 5 transformed world would not be detected, and be treated as the dark matter. According to an astrophysical measurement, the ratio of the dark to ordinary matter in the universe as a whole is almost exactly 5. We expect quarks are insensitive to the triality, and triality will appear as three times larger flavor degrees of freedom in the lattice simulation.

16 pages 8 figures, To be published in International Journal of Modern Physics A

References in corpus (8)

• Phenomenology with Massive Neutrinos
• Sterile neutrino oscillations after first MiniBooNE results
• Study of Non-Standard Neutrino Interactions with Atmospheric Neutrino Data in Super-Kamiokande I and II
• A full parametrization of the 6 X 6 flavor mixing matrix in the presence of three light or heavy sterile neutrinos
• An extension of tribimaximal lepton mixing
• Neutrino masses and mixings in the baryon triality constrained minimal supersymmetric standard model
• Propagator of the lattice domain wall fermion and the staggered fermion
• The magnetic mass of transverse gluon, the B-meson weak decay vertex and the triality symmetry of octonion

Cited by in corpus (10)

• Some properties of dark matter field in the complex octonion space
• Superconducting currents and charge gradients in the octonion spaces
• Axial anomaly and the triality symmetry of octonion
• Precessional angular velocity and field strength in the complex octonion space
• Torques and angular momenta of fluid elements in the octonion spaces
• Color Confinement and Spatial Dimensions in the Complex-sedenion Space
• One underlying mechanism for two piezoelectric effects in the octonion spaces
• Axial anomaly and the triality symmetry of leptons and hadrons
• Spin Angular Momentum of Proton Spin Puzzle in Complex Octonion Spaces
• Cartan's Supersymmetry and Weak and Electromagnetic Interactions