Minimal anomalous U(1)' extension of the MSSM

We study an extension of the minimal supersymmetric standard model by an anomalous Abelian vector multiplet and a Stuckelberg multiplet. The anomalies are cancelled by the Green-Schwarz mechanism and the addition of Chern-Simons terms. The advantage of this choice over the standard one is that it allows for arbitrary values of the quantum numbers of the extra U(1). As a first step toward the study of hadron annihilations producing four leptons in the final state (a clean signal which might be studied at LHC), we then compute the decays Z(')-> Z(0)gamma and Z(')-> Z(0)Z(0). We find that the largest values of the decay rate are similar to 10(-4) GeV, while the expected number of events per year at LHC is at most of the order of 10.