Revisiting the Abelian $N=1$ super Stueckelberg model

The Abelian super Stueckelberg model (ASSM) in the Wess–Zumino (WZ) gauge is revisited, and the actual set of supersymmetric (SUSY) transformation is derived. In particular, we verified that the SUSY transformation of the super Stueckelberg sector compensates the gauge fixing condition imposed on the vector superfield, leading to a mix between the field components of both sectors. We also discuss the possibility to construct an extension of the ASSM with infinite self interacting terms.