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

TL;DR

This paper explores how Cartan's supersymmetry could explain discrepancies between observed meson decay rates and standard model predictions, offering a new perspective on quark contributions and decay processes.

Contribution

It introduces a novel application of Cartan's supersymmetry to meson decays, providing a framework that allows more flexible quark contribution ratios than the standard model.

Findings

Cartan's supersymmetry can account for observed decay branching ratio discrepancies.

The model suggests different quark contribution dominance in $B_s$ and $B_d$ decays.

Potential explanation for $B_d o J/\Psi K_0$ enhancement in high $ riangle t$ regions.

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 $x_\mu, x_{\mu}'$, ($\mu=1,2,3,4$) 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.