Cartan's Supersymmetry and the violation of CP symmetry

TL;DR

This paper explores how Cartan's supersymmetry framework can explain CP violation in B meson decays, linking mathematical structures to observed asymmetries and providing a potential theoretical basis for CP violation phenomena.

Contribution

It extends Cartan's supersymmetry to model CP violation in B meson decays, connecting algebraic structures to experimental asymmetries in particle physics.

Findings

The model predicts CP asymmetry consistent with experimental data.

Asymmetry arises from the $ar s$ and $s$ quark components in B decays.

The approach unifies lepton and quark interactions within Cartan's supersymmetry.

Abstract

Cartan's supersymmetriy fixes couplings of two types of fermions $\psi, \phi$ and two types of vector fields $x_i$ and $x_{i'}$, ($i=1,2,3,4$). The electromagnetic interaction of leptons and quarks is expressed as ${^t\psi}{\mathcal C}x_i\psi$. In the case of coupling of leptons and quarks with $W$, 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 unify the interactions in the form $ {^t\phi}{\mathcal C}\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 $B^0\to K^0\, J/\Psi$, $K^0$ with the $\bar s$ quark dominated by the small component, while in space components of $\bar B^0\to \bar K^0\, J/\Psi$, $\bar K^0$ with the $s$ quark dominated by the small component. This asymmetry could be the origin of the $CP$ asymmetry in 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 study violation of $CP$ symmetry via interference of tree and penguin contributions, and observe that the asymmetry is weak consistent to the experiment.