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The flavor symmetry in the standard model and the triality symmetry
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 , and . 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.Comment: 16 pages 8 figures, To be published in International Journal of
Modern Physics