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Exotic Higgs decays in the E6 inspired SUSY models

We study the decays of the SM-like Higgs state within the E6 inspired supersymmetric (SUSY) models with exact custodial symmetry that forbids tree-level flavor-changing transitions and the most dangerous baryon and lepton number violating operators. In these models there are two states which are absolutely stable and can contribute to the dark matter density. One of them is the lightest SUSY particle (LSP) which is expected to be lighter than 1 eV forming hot dark matter in the Universe. The presence of another stable neutral state allows to account for the observed cold dark matter density. In the considered SUSY models next-to-lightest SUSY particle (NLSP) also tend to be light. We argue that the NLSP with GeV scale mass can result in the substantial branching ratio of the nonstadard decays of the lightest Higgs boson.