  We study the Wess-Zumino model with the coupling extended to a chiral
superfield. In order to incorporate the renormalization effects a further
external real field has to be introduced. It is then possible to derive a
Callan-Symanzik equation and to prove renormalizability. By constructing the
supercurrent in this context the whole machinery for describing the
superconformal symmetries becomes available. The presence of the external
fields allows also to define multiple insertions of all relevant composite
operators. Interesting relations to the curved superspace treatment show up.
