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

In the LHCb detector at CERN, decays of $\chi_b(3P)$ meson to $\Upsilon(1S)\gamma$ and $\Upsilon(2S)\gamma$ are reported at centre-of-mass energy of $\sqrt s=7$ and 8 TeV. Following the success of the assignment of $\chi_b(1P)\to\Upsilon(1S)\gamma$ of the mass of $m(\chi_b(1P))=9.8923$ GeV and $\chi_b(2P)\to\Upsilon(1S)\gamma$ 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 $\Upsilon(mS)$ ($m=1,2$ or 3) and $\bar q q$ which reduces to a $\gamma$, using the Cartan's supersymmetry. Recent non observation of polarizations of $\Upsilon(nS)$ by the CMS collaboration is consistent with the theory.

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