Cartan's Supersymmetry and Weak and Electromagnetic Interactions

We apply the Cartan's supersymmetric model to the weak interaction of hadrons. The electromagnetic currents are transformed by $G_{12},G_{123},G_{13},G_{132}$ and the factor$(1-γ_5)$ is inserted between $l \barν$ or $\bar l ν$ when the photon is replaced by $W^\pm$, and between $l \bar l$ or $ν\bar ν$ when the photon is replaced by $Z$. Electromagnetic currents in the Higgs boson $H^0$ decay into 2$γ$ and $D_s(0^+)$ decay into $D_s(0^-)π$ and $D_s(0^-)γ$ in which leptons are replaced by quarks are also studied. A possibility that the boson near the $B\bar B$ theshold $χ_b(3P, 10.53$ GeV) is the Higgs boson partner $h^0$ is discussed. We adopt Dirac lepton neutrinos and Majorana quark neutrinos, and construct a model that satisfy the $Z_3$ symmetry of the lepton sector and the quark sector, by adding two right-handed neutrinos whose left-handed partner cannot be detected by our electro-magnetic detectors.

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