Light neutralino dark matter in $U(1)_X$SSM

The $U(1)_X$ extension of the minimal supersymmetric standard model(MSSM) is called as $U(1)_X$SSM with the local gauge group $SU(3)_C\times SU(2)_L \times U(1)_Y \times U(1)_X$. $U(1)_X$SSM has three singlet Higgs superfields beyond MSSM. In $U(1)_X$SSM, the mass matrix of neutralino is $8\times8$, whose lightest mass eigenstate possesses cold dark matter characteristic. Supposing the lightest neutralino as dark matter candidate, we study the relic density. For dark matter scattering off nucleus, the cross sections including spin-independent and spin-dependent are both researched. In our numerical results, some parameter space can satisfy the constraints from the relic density and the experiments of dark matter direct detection.