Departure from the Standard Model of Meson Decays and Cartan's Supersymmetry

The experimental decay branching ratios of mesons like $B_s\to \ell\bar \ell$ and $B_d\to \ell\bar \ell$ ($\ell=e$ or $\mu$) do not agree completely with the standard model (SM). Cartan's supersymmetry predicts relation of the coupling of vector particles $x_\mu, x_{\mu}'$, ($\mu=1,2,3,4$) to Dirac spinors of large components $\psi, \phi$ and small components $\mathcal C\psi, \mathcal C\phi$. In the decay of $B_d=\bar b d$, the Cabibbo-Kobayashi-Maskawa(CKM) model suggests that the contribution of $t$ quark dominates, while in the decay of $B_s=\bar b s$, contribution of $c$ quark in the intermediate state is expected to be large, since $s$ and $c$ quark belong to the same CKM sector. The relative strength of the $t$ quark and $c$ quark contribution in Cartan's supersymmetric model has more freedom than that of the SM. Together with the problem of enhancement of $B_d\to J/\Psi K_0$ in high $\Delta t$ region, we can understand the problem of branching ratios of $B$ decay into $e\bar e$ and $\mu\bar\mu$, if the Nature follows Cartan's supersymmetry.