Interactions of exotic neutralino dark matter with nucleons in $U(1)$ extensions of the MSSM originating from $E_6$ GUTs

To ensure anomaly cancellation the $E_6$ inspired $U(1)$ extensions of the minimal supersymmetric (SUSY) standard model (MSSM) involve extra exotic matter. The lightest exotic neutralino in these models can be stable contributing to the cold dark matter density. We consider the interactions of such neutralino with nucleons within a specific extension of the MSSM with an additional $U(1{)}_N$ gauge symmetry (SE${}_6$SSM). The constraints on the couplings of this state, which are set by the present experimental bounds caused by the direct detection experiments, are examined. The obtained results can be generalised to other $E_6$ inspired SUSY models with extra $U(1)$ gauge symmetry.