Axial anomaly and the triality symmetry of leptons and hadrons

TL;DR

This paper explores the application of Cartan's supersymmetric model to pseudoscalar meson decays into photons, linking triality symmetry of octonions to dark matter and meson decay processes.

Contribution

It introduces a novel application of Cartan's supersymmetric framework to meson decay and dark matter, utilizing octonion and quaternion representations and triality symmetry.

Findings

Decays are explained via supersymmetric transformations and triality rules.

Dark matter is interpreted as matter emitting photons in a different triality sector.

The model connects meson decay mechanisms with fundamental symmetry principles.

Abstract

We apply the supersymmetric model of \'E. Cartan to the pseudoscalar meson decay into two photons, $\pi_0\to\gamma\gamma$, $\eta\to\gamma\gamma$ and $\eta'\to\gamma\gamma$. In the book of \'E. Cartan published in 1966, Dirac spinors ${^t(}A,B)$ and ${^t(}C,D)$ and vector fields $E$ and $E'$ were introduced and five supersymmetric transformations $G_{23}, G_{12}, G_{13}, G_{123}$ and $G_{132}$ were considered. The Pauli spinor is treated as a quaternion and the Dirac spinor is treated as an octonion. In the pseudoscalar meson decay, when the two final vector fields belong to the same group ($EE$ or $E'E'$), we call the diagram rescattering diagram. When they belong to different groups ($EE'$), the diagram is called twisted diagram. Assuming the triality selection rules of octonions, dark matter is interpreted as matter emitting photons in a different triality sector than that of electromagnetic probes in our world.