Dark Matter in Anomalous $U(1{)}^{\mathrm{\prime }}$ Models with neutral mixing

We study the lightest masses in the fermionic sector of an anomalous $U(1{)}^{\mathrm{\prime }}$ extension of the minimal supersymmetric standard model inspired by brane constructions. The LSP of this model is an XWIMP (extremely weak interaction particle) which is shown to have a relic density satisfying WMAP data. This computation is carried out numerically after having adapted the DarkSUSY package to our case.