Cartan's Supersymmetry and the Decay of a $h^0$ with the mass $m_{h^0}\simeq 11$GeV to ${\rm Y}(1S)\gamma$ and to ${\rm Y}(nS)\gamma (n=1,2,3)$

Abstract

In the LHCb detector at CERN, decays of ${\chi }_b(3P)$ meson to ${\rm Y}(1S)\gamma$ and ${\rm Y}(2S)\gamma$ are reported at centre-of-mass energy of $\sqrt{s}=7$ and 8 TeV. Following the success of the assignment of ${\chi }_b(1P)\to {\rm Y}(1S)\gamma$ of the mass of $m({\chi }_b(1P))=9.8923$ GeV and ${\chi }_b(2P)\to {\rm Y}(1S)\gamma$ of the mass of $m({\chi }_b(2P))=10.2547$ GeV, the new state ${\chi }_b(3P)$ of the mass of 10.5157 GeV was assigned, but its $J^P$ was not fixed. We study the possibility that this boson is the light Higgs boson $h^0(0^{+})$, and study its decay modes to a $b\bar{b}$ which reduces to an ${\rm Y}(mS)$ ($m=1,2$ or 3) and $\bar{q}q$ which reduces to a $\gamma$, using the Cartan's supersymmetry. Recent non observation of polarizations of ${\rm Y}(nS)$ by the CMS collaboration is consistent with the theory.

Comments: 8 pages, 3 figures. Trilinearities of quark antiquark and ${\rm Y}$ couplings are corrected