Cartan's Supersymmetry and the violation of CP symmetry

Abstract

Cartan's supersymmetriy fixes couplings of two types of fermions $\psi ,\varphi$ and two types of vector fields $x_i$ and $x_{i^{\prime }}$, ($i=1,2,3,4$). 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 ${}^t\varphi \mathcal{C}X\psi$ to ${}^t\varphi \mathcal{C}X(1-{\gamma }_5)\psi$, where $X=x_i$ or ${x_i}^{\prime }$, and unify the interactions in the form ${}^t\varphi \mathcal{C}\overline{x_i}\psi +{}^t\varphi \mathcal{C}\overline{{x_i}^{\prime }}\mathcal{C}\psi$, where $\overline{x_i}$ 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.

17 pages, 12 figures, CP asymmetry plot of B^0 ->J/ΨK decay is added

References in corpus (4)

• Colloquium: Time-reversal violation with quantum-entangled B mesons
• Cartan's Supersymmetry and the Decay of a $H^0(0^{+})$
• Triality selection rules of Octonion and Quantum Mechanics
• Departure from the Standard Model of Meson Decays and Cartan's Supersymmetry

Cited by in corpus (2)

• Triality selection rules of Octonion and Quantum Mechanics
• Departure from the Standard Model of Meson Decays and Cartan's Supersymmetry