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Model Characterization and Dark Matter in the Secluded $U(1)^\prime$ Model

We consider a class of $U(1)^\prime$-extended MSSM in which the $U(1)^{\prime}$ symmetry is broken by vacuum expectation values (VEVs) of four MSSM singlet fields. While one MSSM singlet field interacts with the MSSM Higgs fields, three of them interact only with each other in forming a secluded sector. Assigning universal $U(1)^{\prime}$ charges for three families, the anomaly cancellation condition requires exotic fields which are assumed to be heavy and decoupled. We discuss a variety of $U(1)^{\prime}$ charge assignments and anomaly cancellation, $Z^{\prime}/Z$ hierarchy, neutralinos, charginos and the Higgs sector. We find that the typical spectra involve two CP-odd Higgs bosons lighter than about 200 GeV and 600 GeV respectively, which are mostly formed by the MSSM singlet fields. If the relic density of dark matter is saturated only by a neutralino, compatible solutions predict LSP neutralinos formed by the MSSM singlet fields in the mass scales below about 600 GeV, while it is possible to realize MSSM neutralino LSP above these mass scales. One can classify the implications in three scenarios. Scenario I involves NLSP charginos, while Scenario II involves charginos which do not participate coannihilation processes with the LSP neutralino. These two scenarios predict MSSM singlet LSP neutralinos, while Scenario I leads to larger scattering cross-sections of dark matter. Scenario III has the solutions in which the MSSM neutralinos are considerably involved in LSP decomposition which yields very large scattering cross-section excluded by the direct detection experiments.