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

Abstract

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 $x_{\mu },x_{\mu }^{\prime }$, ($\mu =1,2,3,4$) to Dirac spinors of large components $\psi ,\varphi$ and small components $\mathcal{C}\psi ,\mathcal{C}\varphi$. 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.

18 pages, 7 figures

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• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2016
• Two-Loop Electroweak Corrections for the K -> pi nu anti-nu Decays
• Quark flavour observables in the Littlest Higgs model with T-parity after LHC Run 1
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Cited by in corpus (1)

• Cartan's Supersymmetry and the violation of CP symmetry