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 $\phi$. 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.