Cartan's Supersymmetry and the Decay of a $H^0(0^{+})$

Abstract

We compare the decay of a Higgs boson $H^0(0^{+})\to \ell \bar{\ell }\ell \bar{\ell }\to \gamma \gamma$, $H^0(0^{+})\to W\bar{W}\to \ell \bar{\nu }\bar{\ell }\nu$, and $H^0(0^{+})\to Z\bar{Z}\to \ell \bar{\ell }\ell \bar{\ell }$ using Cartan's supersymmetry, that defines coupling of a vector particle $x_i$ and Dirac spinors $\psi$ and $\varphi$. Apparent discrepancy of $H^0(0^{+})\to \gamma \gamma /\ell \bar{\ell }\ell \bar{\ell }$ experimental data of ATLAS and CMS collaborations disappears, since the sum of transition to $\ell \bar{\ell }\ell \bar{\ell }$ and $\gamma \gamma$ have the meaning. The trilinearity of leptons vector fields coupling and the initial wave functions to be large components define Higgs-leptons couplings. The ratio of Higgs boson decay branching ratios $H\to WW=21.6\pm 0.9$, $H\to \gamma \gamma =0.228\pm 0.011$ can be reproduced when we multiply coupling constant ${\alpha }_s\simeq 1$ for $WW$ and ${\alpha }_e=1/137$ for $\gamma \gamma$ to the number of independent diagrams. Comparison with Atiyah-Witten's quark-gluon dynamics on a manifold of $G_2$ holonomy theory is added.

Comments: 11 pages, 3 figures. Trilinearities of quark anti-quark and vector fields are corrected. Comparison with Atiyah-Witten's quark-gluon dynamics on a manifold of $G_2$ holonomy theory is added