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Cartan's supersymmetriy fixes couplings of two types of fermions $\psi, \phi$and two types of vector fields $x_i$ and $x_{i'}$, ($i=1,2,3,4$). Theelectromagnetic interaction of leptons and quarks is expressed as${^t\psi}{\mathcal C}x_i\psi$. In the case of coupling of leptons and quarkswith $W$, we extend the coupling ${^t\phi}{\mathcal C}X\psi$ to${^t\phi}{\mathcal C}X(1-\gamma_5)\psi$, where $X=x_i$ or ${x_i}'$, and unifythe interactions in the form $ {^t\phi}{\mathcalC}\bar{x_i}\psi+{^t\phi}{\mathcal C} \bar{{x_i}'} {\mathcal C}\psi $, where$\bar{x_i}$ implies appropriate $x_i$ or $(-\gamma_5 x_i)$ is chosen. The$\gamma_5$ term induces in time component of $B^0\to K^0\, J/\Psi$, $K^0$ withthe $\bar s$ quark dominated by the small component, while in space componentsof $\bar B^0\to \bar K^0\, J/\Psi$, $\bar K^0$ with the $s$ quark dominated bythe small component. This asymmetry could be the origin of the $CP$ asymmetryin the $B^0\to K^0\, J/\Psi$.  We apply the model to $B_{s(d)}^0\to D_{s(d)}^- D_{s(d)}^+$ decays and studyviolation of $CP$ symmetry via interference of tree and penguin contributions,and observe that the asymmetry is weak consistent to the experiment.

Cartan's Supersymmetry and the violation of CP symmetry