Minimal Anomalous U(1)' Extension of the MSSM

We study an extension of the MSSM by an anomalous abelian vector multiplet and a St"uckelberg 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 towards 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 $Z^{\mathrm{\prime }}\to Z_0\text{g}$ and $Z’\to Z_0 Z_0$\mathrm{.}Wefindthatthelargestvaluesofthedecayrateis$\sim 10^{-4}$ GeV, while the expected number of events per year at LHC is at most of the order of 10.