Cartan's Supersymmetry and Weak and Electromagnetic Interactions

Abstract

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$(1-\gamma_5)$ is inserted between $l \bar\nu$ or $\bar l \nu$ when the photon is replaced by $W^\pm$, and between $l \bar l$ or $\nu\bar \nu$ when the photon is replaced by $Z$. Electromagnetic currents in the Higgs boson $H^0$ decay into 2$\gamma$ and $D_s(0^+)$ decay into $D_s(0^-)\pi$ and $D_s(0^-)\gamma$ in which leptons are replaced by quarks are also studied. A possibility that the boson near the $B\bar B$ theshold $\chi_b(3P, 10.53$ 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.